Read up/down apex sequences off the un-deduped census
The anchored single-representative reading interacted with dihedral graph dedup to record an arbitrary orientation of each necklace, producing a spurious up-vs-down split at n=9,m=6 (001212 only up, 010122 only down -- the same necklace). Add dihedral_reading_sequences(), which unions the canonical reading over all 2n dihedral anchors and exactly reproduces the brute un-deduped census; make it the default for both experiments, with --anchored to recover the old behaviour. Document the artifact and fix in kempe_sequence_orientation_note.md. Regenerate up + down for n=9, m=3..6. Up and down now agree on sequences and groupings at every m (m=6: identical 31 sequences, 6 groups; the 001212/010122 pair appears on both sides). Groupings coarsen vs anchored (m=4: 3 groups; m=5: 2 groups) since the orientation-honest vocabulary merges previously split sequence-sets. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
+33
-14
@@ -50,6 +50,7 @@ from kempe_up_tooth_sequences import (
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_positions,
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canonical_sequence,
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compact_coloring,
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dihedral_reading_sequences,
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seq_str,
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)
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@@ -101,9 +102,10 @@ class Config:
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class Experiment:
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def __init__(self, n: int, m: int):
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def __init__(self, n: int, m: int, dihedral: bool = True):
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self.n = n
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self.m = m
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self.dihedral = dihedral # read sequences off the un-deduped census
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self.configs: list[Config] = []
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for g in generate(n, min_up_teeth=3, dedup=True):
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for face, edges in inner_face_singletons(g).items():
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@@ -118,13 +120,18 @@ class Experiment:
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self.by_sequence: dict[tuple[int, ...], list[tuple[int, Coloring]]] = defaultdict(list)
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for cidx, cfg in enumerate(self.configs):
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entries: list[tuple[Coloring, tuple[int, ...]]] = []
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entries: list[tuple[Coloring, frozenset]] = []
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seqs: set[tuple[int, ...]] = set()
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for coloring, verdict in classify_colorings(cfg.graph, dedup_colors=True):
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if not verdict.valid:
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continue
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cseq = canonical_sequence(cfg.sequence(coloring))
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entries.append((coloring, cseq))
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if self.dihedral:
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cseqs = dihedral_reading_sequences(cfg.graph.n, coloring,
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cfg.edges, "d")
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else:
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cseqs = {canonical_sequence(cfg.sequence(coloring))}
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entries.append((coloring, frozenset(cseqs)))
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for cseq in cseqs:
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seqs.add(cseq)
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self.by_sequence[cseq].append((cidx, coloring))
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self.colorings.append(entries)
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@@ -223,17 +230,19 @@ def write_sequence_note(exp: Experiment, seq, path, fig_name):
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lines.append("")
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lines.append(
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f"Canonical colour sequence of the singleton down-tooth apexes on a "
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f"single inner non-tooth face (read in increasing annular-edge order, "
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f"reduced modulo the six colour permutations) for Kempe-balanced "
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f"3-colourings of M(T) with **n = {exp.n}**, **m = {exp.m} singleton "
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f"down apexes on the face**."
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f"single inner non-tooth face (read in cyclic order, reduced modulo the "
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f"six colour permutations) for Kempe-balanced 3-colourings of M(T) with "
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f"**n = {exp.n}**, **m = {exp.m} singleton down apexes on the face**. "
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f"Sequences are read off the un-deduped census (every cyclic orientation "
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f"of each colouring), so one colouring may realise several sequences -- "
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f"see `../kempe_sequence_orientation_note.md`."
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)
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lines.append("")
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lines.append(f"- Colour multiset: {counts}.")
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lines.append(f"- Realised by **{len(by_config)}** of {len(exp.configs)} "
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f"configs (M(T), inner face).")
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lines.append(f"- **{len(exp.by_sequence[seq])}** Kempe-balanced colourings "
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f"(mod colour permutation) produce it.")
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f"(mod colour permutation) realise it in some orientation.")
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lines.append(f"- Figure: `{fig_name}` (black rings mark the face's down apexes).")
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lines.append("")
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lines.append("Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` "
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@@ -250,7 +259,8 @@ def write_sequence_note(exp: Experiment, seq, path, fig_name):
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lines.append("")
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for coloring in cols:
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raw = seq_str(cfg.sequence(coloring))
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lines.append(f"- face apexes (raw labels) `{raw}` → canonical `{s}` · "
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lines.append(f"- face apex colours (canonical-rep edge order) `{raw}`, "
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f"realises `{s}` in some orientation · "
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f"`{compact_coloring(cfg.graph, coloring)}`")
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lines.append("")
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with open(path, "w") as fh:
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@@ -263,15 +273,19 @@ def write_summary(exp: Experiment, path):
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lines.append(f"# Inner-face singleton-down-apex sequences of Kempe-balanced "
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f"colourings (n={exp.n}, m={exp.m})")
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lines.append("")
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reading = ("the un-deduped census (every cyclic orientation of each "
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"colouring)" if exp.dihedral
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else "a single anchored representative per dihedral class")
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lines.append(
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f"Every full medial tire graph M(T) with |A(T)| = {exp.n} (one "
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f"representative per dihedral class) that has an inner non-tooth face "
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f"holding exactly {exp.m} singleton down-tooth apexes: "
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f"**{len(exp.configs)} configs (M(T), inner face)**. For each we "
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f"enumerate the Kempe-balanced (valid) proper 3-colourings (modulo "
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f"colour permutation), read the down-apex colour sequence in increasing "
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f"annular-edge order, and reduce it modulo colour permutation (NOT "
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f"dihedral symmetry)."
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f"colour permutation), read the down-apex colour sequence in cyclic "
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f"order off {reading}, and reduce it modulo colour permutation (NOT "
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f"dihedral symmetry). Reading off the census makes the recorded "
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f"vocabulary orientation-honest; see `../kempe_sequence_orientation_note.md`."
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)
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lines.append("")
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total = sum(len(c) for c in exp.colorings)
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@@ -349,7 +363,9 @@ def write_summary(exp: Experiment, path):
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# ---------------------------------------------------------------------------
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def run(args):
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exp = Experiment(args.n, args.m)
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exp = Experiment(args.n, args.m, dihedral=not args.anchored)
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mode = "anchored" if args.anchored else "census (orientation-honest)"
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print(f"reading: {mode}")
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print(f"n={args.n}, m={args.m}: {len(exp.configs)} configs (M(T), inner face)")
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print(f"distinct canonical down-apex sequences: {len(exp.by_sequence)}")
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for seq in exp.sequences():
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@@ -377,6 +393,9 @@ def main():
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parser.add_argument("--m", type=int, default=3,
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help="singleton down apexes on the inner face (>=3)")
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parser.add_argument("--no-figures", action="store_true")
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parser.add_argument("--anchored", action="store_true",
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help="read one anchored representative per class "
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"(old behaviour) instead of the un-deduped census")
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run(parser.parse_args())
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+243
-243
@@ -1,10 +1,10 @@
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# Inner-face down-apex sequence `012`
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Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 3 singleton down apexes on the face**.
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Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 3 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
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- Colour multiset: 1×colour0, 1×colour1, 1×colour2.
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- Realised by **26** of 26 configs (M(T), inner face).
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- **241** Kempe-balanced colourings (mod colour permutation) produce it.
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- **241** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
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- Figure: `seq_012.png` (black rings mark the face's down apexes).
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Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
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@@ -13,370 +13,370 @@ Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D
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22 colouring(s) with down-apex sequence `012`:
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- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u2:2 u3:2 u4:2 u5:2] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010101021 U[u0:2 u1:2 u2:2 u3:2 u4:2 u5:2] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=010102012 U[u0:2 u1:2 u2:2 u3:2 u4:1 u5:1] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010102021 U[u0:2 u1:2 u2:2 u3:2 u4:1 u5:1] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=010121012 U[u0:2 u1:2 u2:2 u3:0 u4:0 u5:2] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010121021 U[u0:2 u1:2 u2:2 u3:0 u4:0 u5:2] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=010201012 U[u0:2 u1:2 u2:1 u3:1 u4:2 u5:2] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010201021 U[u0:2 u1:2 u2:1 u3:1 u4:2 u5:2] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=010202012 U[u0:2 u1:2 u2:1 u3:1 u4:1 u5:1] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u2:1 u3:1 u4:1 u5:1] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=010212012 U[u0:2 u1:2 u2:1 u3:0 u4:0 u5:1] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010212021 U[u0:2 u1:2 u2:1 u3:0 u4:0 u5:1] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012012012 U[u0:2 u1:0 u2:1 u3:2 u4:0 u5:1] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=012012021 U[u0:2 u1:0 u2:1 u3:2 u4:0 u5:1] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012021012 U[u0:2 u1:0 u2:1 u3:1 u4:0 u5:2] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=012021021 U[u0:2 u1:0 u2:1 u3:1 u4:0 u5:2] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012101012 U[u0:2 u1:0 u2:0 u3:2 u4:2 u5:2] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=012101021 U[u0:2 u1:0 u2:0 u3:2 u4:2 u5:2] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012102012 U[u0:2 u1:0 u2:0 u3:2 u4:1 u5:1] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=012102021 U[u0:2 u1:0 u2:0 u3:2 u4:1 u5:1] D[d6:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012121012 U[u0:2 u1:0 u2:0 u3:0 u4:0 u5:2] D[d6:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=012121021 U[u0:2 u1:0 u2:0 u3:0 u4:0 u5:2] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2 u4:2 u5:2] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u3:2 u4:2 u5:2] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u3:2 u4:1 u5:1] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2 u4:1 u5:1] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u3:0 u4:0 u5:2] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u3:0 u4:0 u5:2] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1 u4:2 u5:2] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u3:1 u4:2 u5:2] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u3:1 u4:1 u5:1] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1 u4:1 u5:1] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u3:0 u4:0 u5:1] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u3:0 u4:0 u5:1] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012012012 U[u0:2 u1:0 u2:1 u3:2 u4:0 u5:1] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1 u3:2 u4:0 u5:1] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1 u3:1 u4:0 u5:2] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012021021 U[u0:2 u1:0 u2:1 u3:1 u4:0 u5:2] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2 u4:2 u5:2] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u3:2 u4:2 u5:2] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u3:2 u4:1 u5:1] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2 u4:1 u5:1] D[d6:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u3:0 u4:0 u5:2] D[d6:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u3:0 u4:0 u5:2] D[d6:1 d7:0 d8:2]`
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## C01 — word=UUUUUDUDD bites=- face=root apexes=[d5,d7,d8]
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11 colouring(s) with down-apex sequence `012`:
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- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u2:2 u3:2 u4:2 u6:2] D[d5:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010102021 U[u0:2 u1:2 u2:2 u3:2 u4:1 u6:1] D[d5:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=010121012 U[u0:2 u1:2 u2:2 u3:0 u4:0 u6:2] D[d5:2 d7:0 d8:1]`
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- face apexes (raw labels) `201` → canonical `012` · `A=010201012 U[u0:2 u1:2 u2:1 u3:1 u4:2 u6:2] D[d5:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u2:1 u3:1 u4:1 u6:1] D[d5:1 d7:0 d8:2]`
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- face apexes (raw labels) `102` → canonical `012` · `A=010212021 U[u0:2 u1:2 u2:1 u3:0 u4:0 u6:1] D[d5:1 d7:0 d8:2]`
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- face apexes (raw labels) `102` → canonical `012` · `A=012012021 U[u0:2 u1:0 u2:1 u3:2 u4:0 u6:1] D[d5:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012021012 U[u0:2 u1:0 u2:1 u3:1 u4:0 u6:2] D[d5:2 d7:0 d8:1]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012101012 U[u0:2 u1:0 u2:0 u3:2 u4:2 u6:2] D[d5:2 d7:0 d8:1]`
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- face apexes (raw labels) `102` → canonical `012` · `A=012102021 U[u0:2 u1:0 u2:0 u3:2 u4:1 u6:1] D[d5:1 d7:0 d8:2]`
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- face apexes (raw labels) `201` → canonical `012` · `A=012121012 U[u0:2 u1:0 u2:0 u3:0 u4:0 u6:2] D[d5:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2 u4:2 u6:2] D[d5:2 d7:0 d8:1]`
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- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2 u4:1 u6:1] D[d5:1 d7:0 d8:2]`
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- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u3:0 u4:0 u6:2] D[d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1 u4:2 u6:2] D[d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1 u4:1 u6:1] D[d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u3:0 u4:0 u6:1] D[d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1 u3:2 u4:0 u6:1] D[d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1 u3:1 u4:0 u6:2] D[d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2 u4:2 u6:2] D[d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2 u4:1 u6:1] D[d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u3:0 u4:0 u6:2] D[d5:2 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUUDUUDD bites=- face=root apexes=[d4,d7,d8]
|
||||
|
||||
17 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u2:2 u3:2 u5:2 u6:2] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101212 U[u0:2 u1:2 u2:2 u3:2 u5:0 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010102021 U[u0:2 u1:2 u2:2 u3:2 u5:1 u6:1] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010102121 U[u0:2 u1:2 u2:2 u3:2 u5:0 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010120121 U[u0:2 u1:2 u2:2 u3:0 u5:2 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010201012 U[u0:2 u1:2 u2:1 u3:1 u5:2 u6:2] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010201212 U[u0:2 u1:2 u2:1 u3:1 u5:0 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u2:1 u3:1 u5:1 u6:1] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202121 U[u0:2 u1:2 u2:1 u3:1 u5:0 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010210212 U[u0:2 u1:2 u2:1 u3:0 u5:1 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012010212 U[u0:2 u1:0 u2:1 u3:2 u5:1 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012020121 U[u0:2 u1:0 u2:1 u3:1 u5:2 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101012 U[u0:2 u1:0 u2:0 u3:2 u5:2 u6:2] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101212 U[u0:2 u1:0 u2:0 u3:2 u5:0 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012102021 U[u0:2 u1:0 u2:0 u3:2 u5:1 u6:1] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012102121 U[u0:2 u1:0 u2:0 u3:2 u5:0 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012120121 U[u0:2 u1:0 u2:0 u3:0 u5:2 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2 u5:2 u6:2] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u3:2 u5:0 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2 u5:1 u6:1] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u3:2 u5:0 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u3:0 u5:2 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1 u5:2 u6:2] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u3:1 u5:0 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1 u5:1 u6:1] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u3:1 u5:0 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u3:0 u5:1 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012010212 U[u0:2 u1:0 u2:1 u3:2 u5:1 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012020121 U[u0:2 u1:0 u2:1 u3:1 u5:2 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2 u5:2 u6:2] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u3:2 u5:0 u6:0] D[d4:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2 u5:1 u6:1] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u3:2 u5:0 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u3:0 u5:2 u6:0] D[d4:1 d7:0 d8:2]`
|
||||
|
||||
## C03 — word=UUUUDUDUD bites=- face=root apexes=[d4,d6,d8]
|
||||
|
||||
26 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101212 U[u0:2 u1:2 u2:2 u3:2 u5:0 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010102121 U[u0:2 u1:2 u2:2 u3:2 u5:0 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010120121 U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010121012 U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010121021 U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010121201 U[u0:2 u1:2 u2:2 u3:0 u5:0 u7:2] D[d4:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010201212 U[u0:2 u1:2 u2:1 u3:1 u5:0 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202121 U[u0:2 u1:2 u2:1 u3:1 u5:0 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010210212 U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010212012 U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010212021 U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010212102 U[u0:2 u1:2 u2:1 u3:0 u5:0 u7:1] D[d4:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012010212 U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012012012 U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012012021 U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012012102 U[u0:2 u1:0 u2:1 u3:2 u5:0 u7:1] D[d4:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012020121 U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012021012 U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012021021 U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012021201 U[u0:2 u1:0 u2:1 u3:1 u5:0 u7:2] D[d4:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101212 U[u0:2 u1:0 u2:0 u3:2 u5:0 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012102121 U[u0:2 u1:0 u2:0 u3:2 u5:0 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012120121 U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012121012 U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012121021 U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012121201 U[u0:2 u1:0 u2:0 u3:0 u5:0 u7:2] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u3:2 u5:0 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u3:2 u5:0 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u3:0 u5:0 u7:2] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u3:1 u5:0 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u3:1 u5:0 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u3:0 u5:0 u7:1] D[d4:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012010212 U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012012012 U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012012102 U[u0:2 u1:0 u2:1 u3:2 u5:0 u7:1] D[d4:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012020121 U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012021021 U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012021201 U[u0:2 u1:0 u2:1 u3:1 u5:0 u7:2] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u3:2 u5:0 u7:0] D[d4:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u3:2 u5:0 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0] D[d4:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0] D[d4:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0] D[d4:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u3:0 u5:0 u7:2] D[d4:0 d6:1 d8:2]`
|
||||
|
||||
## C04 — word=UUUUDDDDD bites=(4,8) face=bite(4,8) apexes=[d5,d6,d7]
|
||||
|
||||
12 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d5:2 d6:1 d7:0 p4_8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d5:0 d6:1 d7:2 p4_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d5:1 d6:2 d7:0 p4_8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d5:0 d6:2 d7:1 p4_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d5:2 d6:1 d7:0 p4_8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d5:0 d6:1 d7:2 p4_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d5:1 d6:2 d7:0 p4_8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d5:0 d6:2 d7:1 p4_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d5:2 d6:1 d7:0 p4_8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d5:0 d6:1 d7:2 p4_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d5:1 d6:2 d7:0 p4_8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d5:0 d6:2 d7:1 p4_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d5:2 d6:1 d7:0 p4_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d5:0 d6:1 d7:2 p4_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d5:1 d6:2 d7:0 p4_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d5:0 d6:2 d7:1 p4_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d5:2 d6:1 d7:0 p4_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d5:0 d6:1 d7:2 p4_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d5:1 d6:2 d7:0 p4_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d5:0 d6:2 d7:1 p4_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d5:2 d6:1 d7:0 p4_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d5:0 d6:1 d7:2 p4_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d5:1 d6:2 d7:0 p4_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d5:0 d6:2 d7:1 p4_8:1]`
|
||||
|
||||
## C05 — word=UUUDUUUDD bites=- face=root apexes=[d3,d7,d8]
|
||||
|
||||
13 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u2:2 u4:2 u5:2 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101212 U[u0:2 u1:2 u2:2 u4:2 u5:0 u6:0] D[d3:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010102012 U[u0:2 u1:2 u2:2 u4:1 u5:1 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010201021 U[u0:2 u1:2 u2:1 u4:2 u5:2 u6:1] D[d3:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u2:1 u4:1 u5:1 u6:1] D[d3:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202121 U[u0:2 u1:2 u2:1 u4:1 u5:0 u6:0] D[d3:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012010212 U[u0:2 u1:0 u2:1 u4:2 u5:1 u6:0] D[d3:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012012012 U[u0:2 u1:0 u2:1 u4:0 u5:1 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012020121 U[u0:2 u1:0 u2:1 u4:1 u5:2 u6:0] D[d3:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012021021 U[u0:2 u1:0 u2:1 u4:0 u5:2 u6:1] D[d3:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101012 U[u0:2 u1:0 u2:0 u4:2 u5:2 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101212 U[u0:2 u1:0 u2:0 u4:2 u5:0 u6:0] D[d3:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012102012 U[u0:2 u1:0 u2:0 u4:1 u5:1 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u4:2 u5:2 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u4:2 u5:0 u6:0] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u4:1 u5:1 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u4:2 u5:2 u6:1] D[d3:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u4:1 u5:1 u6:1] D[d3:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u4:1 u5:0 u6:0] D[d3:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012010212 U[u0:2 u1:0 u2:1 u4:2 u5:1 u6:0] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012012012 U[u0:2 u1:0 u2:1 u4:0 u5:1 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012020121 U[u0:2 u1:0 u2:1 u4:1 u5:2 u6:0] D[d3:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012021021 U[u0:2 u1:0 u2:1 u4:0 u5:2 u6:1] D[d3:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u4:2 u5:2 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u4:2 u5:0 u6:0] D[d3:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u4:1 u5:1 u6:2] D[d3:2 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UUUDUUDUD bites=- face=root apexes=[d3,d6,d8]
|
||||
|
||||
20 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101212 U[u0:2 u1:2 u2:2 u4:2 u5:0 u7:0] D[d3:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010120102 U[u0:2 u1:2 u2:2 u4:1 u5:2 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010120201 U[u0:2 u1:2 u2:2 u4:1 u5:1 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010121012 U[u0:2 u1:2 u2:2 u4:0 u5:2 u7:0] D[d3:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010121021 U[u0:2 u1:2 u2:2 u4:0 u5:2 u7:0] D[d3:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010121201 U[u0:2 u1:2 u2:2 u4:0 u5:0 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202121 U[u0:2 u1:2 u2:1 u4:1 u5:0 u7:0] D[d3:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010210102 U[u0:2 u1:2 u2:1 u4:2 u5:2 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010210201 U[u0:2 u1:2 u2:1 u4:2 u5:1 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010212012 U[u0:2 u1:2 u2:1 u4:0 u5:1 u7:0] D[d3:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010212021 U[u0:2 u1:2 u2:1 u4:0 u5:1 u7:0] D[d3:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010212102 U[u0:2 u1:2 u2:1 u4:0 u5:0 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012010212 U[u0:2 u1:0 u2:1 u4:2 u5:1 u7:0] D[d3:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012020121 U[u0:2 u1:0 u2:1 u4:1 u5:2 u7:0] D[d3:1 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101212 U[u0:2 u1:0 u2:0 u4:2 u5:0 u7:0] D[d3:2 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012120102 U[u0:2 u1:0 u2:0 u4:1 u5:2 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012120201 U[u0:2 u1:0 u2:0 u4:1 u5:1 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012121012 U[u0:2 u1:0 u2:0 u4:0 u5:2 u7:0] D[d3:0 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012121021 U[u0:2 u1:0 u2:0 u4:0 u5:2 u7:0] D[d3:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012121201 U[u0:2 u1:0 u2:0 u4:0 u5:0 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u4:2 u5:0 u7:0] D[d3:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u4:1 u5:2 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010120201 U[u0:2 u1:2 u2:2 u4:1 u5:1 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u4:0 u5:2 u7:0] D[d3:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u4:0 u5:2 u7:0] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u4:0 u5:0 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u4:1 u5:0 u7:0] D[d3:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010210102 U[u0:2 u1:2 u2:1 u4:2 u5:2 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u4:2 u5:1 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u4:0 u5:1 u7:0] D[d3:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u4:0 u5:1 u7:0] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u4:0 u5:0 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012010212 U[u0:2 u1:0 u2:1 u4:2 u5:1 u7:0] D[d3:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012020121 U[u0:2 u1:0 u2:1 u4:1 u5:2 u7:0] D[d3:1 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u4:2 u5:0 u7:0] D[d3:2 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u4:1 u5:2 u7:1] D[d3:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012120201 U[u0:2 u1:0 u2:0 u4:1 u5:1 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u4:0 u5:2 u7:0] D[d3:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u4:0 u5:2 u7:0] D[d3:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u4:0 u5:0 u7:2] D[d3:0 d6:1 d8:2]`
|
||||
|
||||
## C07 — word=UUUDUDDDD bites=(3,5) face=root apexes=[d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d6:2 d7:0 d8:1 p3_5:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d6:1 d7:0 d8:2 p3_5:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d6:2 d7:0 d8:1 p3_5:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d6:1 d7:0 d8:2 p3_5:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d6:2 d7:0 d8:1 p3_5:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d6:1 d7:0 d8:2 p3_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d6:2 d7:0 d8:1 p3_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d6:1 d7:0 d8:2 p3_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d6:2 d7:0 d8:1 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d6:1 d7:0 d8:2 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d6:2 d7:0 d8:1 p3_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d6:1 d7:0 d8:2 p3_5:2]`
|
||||
|
||||
## C08 — word=UUUDUDDDD bites=(3,8) face=bite(3,8) apexes=[d5,d6,d7]
|
||||
|
||||
6 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d5:2 d6:1 d7:0 p3_8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d5:0 d6:1 d7:2 p3_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d5:1 d6:2 d7:0 p3_8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d5:0 d6:2 d7:1 p3_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d5:2 d6:1 d7:0 p3_8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d5:0 d6:1 d7:2 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d5:2 d6:1 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d5:0 d6:1 d7:2 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d5:1 d6:2 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d5:0 d6:2 d7:1 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d5:2 d6:1 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d5:0 d6:1 d7:2 p3_8:2]`
|
||||
|
||||
## C09 — word=UUUDDUDDD bites=(4,6) face=root apexes=[d3,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d7:0 d8:1 p4_6:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d7:0 d8:2 p4_6:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d7:0 d8:1 p4_6:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d7:0 d8:1 p4_6:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d7:0 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d7:0 d8:1 p4_6:2]`
|
||||
|
||||
## C10 — word=UUUDDUDDD bites=(3,8) face=bite(3,8) apexes=[d4,d6,d7]
|
||||
|
||||
3 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d4:2 d6:1 d7:0 p3_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d4:1 d6:2 d7:0 p3_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d4:2 d6:1 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d4:2 d6:1 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d4:1 d6:2 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d4:2 d6:1 d7:0 p3_8:2]`
|
||||
|
||||
## C11 — word=UUDUUDUUD bites=- face=root apexes=[d2,d5,d8]
|
||||
|
||||
18 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101202 U[u0:2 u1:2 u3:2 u4:2 u6:1 u7:1] D[d2:2 d5:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101212 U[u0:2 u1:2 u3:2 u4:2 u6:0 u7:0] D[d2:2 d5:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010102102 U[u0:2 u1:2 u3:2 u4:1 u6:2 u7:1] D[d2:2 d5:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121202 U[u0:2 u1:2 u3:0 u4:0 u6:1 u7:1] D[d2:2 d5:0 d8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121212 U[u0:2 u1:2 u3:0 u4:0 u6:0 u7:0] D[d2:2 d5:0 d8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010201201 U[u0:2 u1:2 u3:1 u4:2 u6:1 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202101 U[u0:2 u1:2 u3:1 u4:1 u6:2 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202121 U[u0:2 u1:2 u3:1 u4:1 u6:0 u7:0] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010212101 U[u0:2 u1:2 u3:0 u4:0 u6:2 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010212121 U[u0:2 u1:2 u3:0 u4:0 u6:0 u7:0] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012012101 U[u0:2 u1:0 u3:2 u4:0 u6:2 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012012121 U[u0:2 u1:0 u3:2 u4:0 u6:0 u7:0] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012021201 U[u0:2 u1:0 u3:1 u4:0 u6:1 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012101012 U[u0:2 u1:0 u3:2 u4:2 u6:2 u7:0] D[d2:0 d5:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012102021 U[u0:2 u1:0 u3:2 u4:1 u6:1 u7:0] D[d2:0 d5:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012120102 U[u0:2 u1:0 u3:0 u4:1 u6:2 u7:1] D[d2:0 d5:2 d8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012120201 U[u0:2 u1:0 u3:0 u4:1 u6:1 u7:2] D[d2:0 d5:1 d8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012121012 U[u0:2 u1:0 u3:0 u4:0 u6:2 u7:0] D[d2:0 d5:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u4:2 u6:1 u7:1] D[d2:2 d5:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101212 U[u0:2 u1:2 u3:2 u4:2 u6:0 u7:0] D[d2:2 d5:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010102102 U[u0:2 u1:2 u3:2 u4:1 u6:2 u7:1] D[d2:2 d5:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u4:0 u6:1 u7:1] D[d2:2 d5:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u4:0 u6:0 u7:0] D[d2:2 d5:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010201201 U[u0:2 u1:2 u3:1 u4:2 u6:1 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u4:1 u6:2 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202121 U[u0:2 u1:2 u3:1 u4:1 u6:0 u7:0] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u4:0 u6:2 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u4:0 u6:0 u7:0] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u4:0 u6:2 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u4:0 u6:0 u7:0] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012021201 U[u0:2 u1:0 u3:1 u4:0 u6:1 u7:2] D[d2:1 d5:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012101012 U[u0:2 u1:0 u3:2 u4:2 u6:2 u7:0] D[d2:0 d5:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012102021 U[u0:2 u1:0 u3:2 u4:1 u6:1 u7:0] D[d2:0 d5:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u4:1 u6:2 u7:1] D[d2:0 d5:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012120201 U[u0:2 u1:0 u3:0 u4:1 u6:1 u7:2] D[d2:0 d5:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u4:0 u6:2 u7:0] D[d2:0 d5:2 d8:1]`
|
||||
|
||||
## C12 — word=UUDUUDDDD bites=(2,5) face=root apexes=[d6,d7,d8]
|
||||
|
||||
10 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d6:2 d7:0 d8:1 p2_5:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d6:1 d7:0 d8:2 p2_5:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d6:2 d7:0 d8:1 p2_5:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d6:1 d7:0 d8:2 p2_5:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d6:2 d7:0 d8:1 p2_5:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d6:1 d7:0 d8:2 p2_5:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d6:2 d7:0 d8:1 p2_5:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d6:1 d7:0 d8:2 p2_5:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d6:2 d7:0 d8:1 p2_5:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d6:1 d7:0 d8:2 p2_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d6:2 d7:0 d8:1 p2_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d6:1 d7:0 d8:2 p2_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d6:2 d7:0 d8:1 p2_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d6:1 d7:0 d8:2 p2_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d6:2 d7:0 d8:1 p2_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d6:1 d7:0 d8:2 p2_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d6:2 d7:0 d8:1 p2_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d6:1 d7:0 d8:2 p2_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d6:2 d7:0 d8:1 p2_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d6:1 d7:0 d8:2 p2_5:1]`
|
||||
|
||||
## C13 — word=UUDUDUDDD bites=(4,6) face=root apexes=[d2,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d7:0 d8:1 p4_6:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d7:0 d8:1 p4_6:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d7:0 d8:2 p4_6:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d7:0 d8:2 p4_6:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d7:0 d8:2 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d7:0 d8:1 p4_6:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d7:0 d8:1 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d7:0 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d7:0 d8:2 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d7:0 d8:2 p4_6:0]`
|
||||
|
||||
## C14 — word=UUDUDUDDD bites=(2,4) face=root apexes=[d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d6:2 d7:0 d8:1 p2_4:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d6:1 d7:0 d8:2 p2_4:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d6:2 d7:0 d8:1 p2_4:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d6:1 d7:0 d8:2 p2_4:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d6:2 d7:0 d8:1 p2_4:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d6:1 d7:0 d8:2 p2_4:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d6:2 d7:0 d8:1 p2_4:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d6:1 d7:0 d8:2 p2_4:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d6:2 d7:0 d8:1 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d6:1 d7:0 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d6:2 d7:0 d8:1 p2_4:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d6:1 d7:0 d8:2 p2_4:0]`
|
||||
|
||||
## C15 — word=UUDUDUDDD bites=(2,8) face=bite(2,8) apexes=[d4,d6,d7]
|
||||
|
||||
5 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d4:2 d6:1 d7:0 p2_8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d4:0 d6:1 d7:2 p2_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d4:1 d6:2 d7:0 p2_8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d4:0 d6:2 d7:1 p2_8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d4:0 d6:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d4:2 d6:1 d7:0 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d4:0 d6:1 d7:2 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d4:1 d6:2 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d4:0 d6:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d4:0 d6:2 d7:1 p2_8:1]`
|
||||
|
||||
## C16 — word=UUDUDDUDD bites=(5,7) face=root apexes=[d2,d4,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d8:1 p5_7:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d8:2 p5_7:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d8:2 p5_7:0]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d8:1 p5_7:0]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d8:2 p5_7:0]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d8:2 p5_7:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d8:2 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d8:2 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d8:2 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d8:2 p5_7:2]`
|
||||
|
||||
## C17 — word=UUDUDDUDD bites=(2,4) face=root apexes=[d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d5:2 d7:0 d8:1 p2_4:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d5:1 d7:0 d8:2 p2_4:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d5:2 d7:0 d8:1 p2_4:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d5:2 d7:0 d8:1 p2_4:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d5:1 d7:0 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d5:2 d7:0 d8:1 p2_4:0]`
|
||||
|
||||
## C18 — word=UUDUDDUDD bites=(2,8) face=bite(2,8) apexes=[d4,d5,d7]
|
||||
|
||||
5 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d4:1 d5:0 d7:2 p2_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d4:1 d5:2 d7:0 p2_8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d4:2 d5:0 d7:1 p2_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d4:2 d5:1 d7:0 p2_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d4:2 d5:1 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d4:1 d5:0 d7:2 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d4:1 d5:2 d7:0 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d4:2 d5:0 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d4:2 d5:1 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d4:2 d5:1 d7:0 p2_8:1]`
|
||||
|
||||
## C19 — word=UUDUDDDUD bites=(6,8) face=root apexes=[d2,d4,d5]
|
||||
|
||||
3 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 p6_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 p6_8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 p6_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 p6_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 p6_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 p6_8:2]`
|
||||
|
||||
## C20 — word=UUDUDDDUD bites=(2,8) face=bite(2,8) apexes=[d4,d5,d6]
|
||||
|
||||
10 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d4:2 d5:0 d6:1 p2_8:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d4:1 d5:0 d6:2 p2_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d4:1 d5:2 d6:0 p2_8:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d4:0 d5:2 d6:1 p2_8:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d4:2 d5:0 d6:1 p2_8:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d4:1 d5:0 d6:2 p2_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d4:2 d5:1 d6:0 p2_8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d4:0 d5:1 d6:2 p2_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d4:2 d5:1 d6:0 p2_8:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d4:0 d5:1 d6:2 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d4:2 d5:0 d6:1 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d4:1 d5:0 d6:2 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d4:1 d5:2 d6:0 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d4:0 d5:2 d6:1 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d4:2 d5:0 d6:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d4:1 d5:0 d6:2 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d4:2 d5:1 d6:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d4:0 d5:1 d6:2 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d4:2 d5:1 d6:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d4:0 d5:1 d6:2 p2_8:1]`
|
||||
|
||||
## C21 — word=UUDDUUDDD bites=(3,6) face=root apexes=[d2,d7,d8]
|
||||
|
||||
9 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d7:0 d8:1 p3_6:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d7:0 d8:1 p3_6:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d7:0 d8:1 p3_6:0]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d7:0 d8:1 p3_6:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d7:0 d8:2 p3_6:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d7:0 d8:2 p3_6:1]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d7:0 d8:2 p3_6:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d7:0 d8:2 p3_6:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d7:0 d8:2 p3_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d7:0 d8:1 p3_6:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d7:0 d8:1 p3_6:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d7:0 d8:1 p3_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d7:0 d8:1 p3_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d7:0 d8:2 p3_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d7:0 d8:2 p3_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d7:0 d8:2 p3_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d7:0 d8:2 p3_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d7:0 d8:2 p3_6:1]`
|
||||
|
||||
## C22 — word=UUDDUDUDD bites=(5,7) face=root apexes=[d2,d3,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d8:1 p5_7:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d8:1 p5_7:0]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d8:2 p5_7:2]`
|
||||
- face apexes (raw labels) `102` → canonical `012` · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d8:2 p5_7:0]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d8:2 p5_7:2]`
|
||||
- face apex colours (canonical-rep edge order) `102`, realises `012` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d8:2 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d8:1 p5_7:0]`
|
||||
|
||||
## C23 — word=UUDDUDUDD bites=(2,8) face=bite(2,8) apexes=[d3,d5,d7]
|
||||
|
||||
8 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d3:2 d5:1 d7:0 p2_8:2]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d3:0 d5:1 d7:2 p2_8:2]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d3:1 d5:2 d7:0 p2_8:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d3:0 d5:2 d7:1 p2_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d3:2 d5:1 d7:0 p2_8:1]`
|
||||
- face apexes (raw labels) `210` → canonical `012` · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d3:2 d5:1 d7:0 p2_8:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d3:2 d5:0 d7:1 p2_8:1]`
|
||||
- face apexes (raw labels) `120` → canonical `012` · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d3:1 d5:2 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d3:2 d5:1 d7:0 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d3:0 d5:1 d7:2 p2_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d3:1 d5:2 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d3:0 d5:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d3:2 d5:1 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210`, realises `012` in some orientation · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d3:2 d5:1 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d3:2 d5:0 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `120`, realises `012` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d3:1 d5:2 d7:0 p2_8:1]`
|
||||
|
||||
## C24 — word=UDUDUDUDD bites=(5,7) face=root apexes=[d1,d3,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d8:1 p5_7:1]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d8:1 p5_7:0]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d8:1 p5_7:1]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d8:1 p5_7:1]`
|
||||
- face apexes (raw labels) `012` → canonical `012` · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d8:2 p5_7:2]`
|
||||
- face apexes (raw labels) `021` → canonical `012` · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `012`, realises `012` in some orientation · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d8:2 p5_7:2]`
|
||||
- face apex colours (canonical-rep edge order) `021`, realises `012` in some orientation · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d8:1 p5_7:0]`
|
||||
|
||||
## C25 — word=UDUDUDUDD bites=(3,5) face=root apexes=[d1,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `012`:
|
||||
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d7:0 d8:1 p3_5:2]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d7:0 d8:1 p3_5:0]`
|
||||
- face apexes (raw labels) `201` → canonical `012` · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d7:0 d8:1 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d7:0 d8:1 p3_5:2]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d7:0 d8:1 p3_5:0]`
|
||||
- face apex colours (canonical-rep edge order) `201`, realises `012` in some orientation · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d7:0 d8:1 p3_5:1]`
|
||||
|
||||
|
||||
BIN
Binary file not shown.
+1
-1
@@ -1,6 +1,6 @@
|
||||
# Inner-face singleton-down-apex sequences of Kempe-balanced colourings (n=9, m=3)
|
||||
|
||||
Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedral class) that has an inner non-tooth face holding exactly 3 singleton down-tooth apexes: **26 configs (M(T), inner face)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the down-apex colour sequence in increasing annular-edge order, and reduce it modulo colour permutation (NOT dihedral symmetry).
|
||||
Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedral class) that has an inner non-tooth face holding exactly 3 singleton down-tooth apexes: **26 configs (M(T), inner face)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the down-apex colour sequence in cyclic order off the un-deduped census (every cyclic orientation of each colouring), and reduce it modulo colour permutation (NOT dihedral symmetry). Reading off the census makes the recorded vocabulary orientation-honest; see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Total Kempe-balanced colourings (mod colour permutation): **241**.
|
||||
- Distinct canonical down-apex sequences overall: **1**.
|
||||
|
||||
+66
-66
@@ -1,10 +1,10 @@
|
||||
# Inner-face down-apex sequence `0000`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0.
|
||||
- Realised by **21** of 23 configs (M(T), inner face).
|
||||
- **64** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **64** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_0000.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
@@ -13,168 +13,168 @@ Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D
|
||||
|
||||
10 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010120101 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010120202 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010210101 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010210202 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012010202 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012020101 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012120101 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012120202 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010120101 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010120202 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010210101 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010210202 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012120101 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012120202 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C01 — word=UUUUDUDDD bites=- face=root apexes=[d4,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010120202 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010210101 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012120202 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010120202 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010210101 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012120202 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C02 — word=UUUUDDUDD bites=- face=root apexes=[d4,d5,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010120202 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010210101 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:2 d5:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:2 d5:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012120202 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010120202 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010210101 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:2 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:2 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012120202 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:1 d5:1 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUUDUUDDD bites=- face=root apexes=[d3,d6,d7,d8]
|
||||
|
||||
7 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010102101 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010201202 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012012101 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012021202 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012102101 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010102101 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010201202 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012102101 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C04 — word=UUUDUDUDD bites=- face=root apexes=[d3,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1 u4:2 u6:2] D[d3:2 d5:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1 u4:1 u6:1] D[d3:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1 u4:2 u6:2] D[d3:2 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1 u4:1 u6:1] D[d3:1 d5:1 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UUUDUDDUD bites=- face=root apexes=[d3,d5,d6,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1 u4:2 u7:2] D[d3:2 d5:2 d6:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1 u4:1 u7:1] D[d3:1 d5:1 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1 u4:2 u7:2] D[d3:2 d5:2 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1 u4:1 u7:1] D[d3:1 d5:1 d6:1 d8:1]`
|
||||
|
||||
## C06 — word=UUUDDUUDD bites=- face=root apexes=[d3,d4,d7,d8]
|
||||
|
||||
7 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010101201 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010202102 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:1 d4:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010201 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020102 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:1 d4:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012101201 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:1 d4:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:1 d4:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:2 d4:2 d7:2 d8:2]`
|
||||
|
||||
## C07 — word=UUUDDDDDD bites=(3,8) face=bite(3,8) apexes=[d4,d5,d6,d7]
|
||||
|
||||
4 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012010101 U[u0:2 u1:0 u2:1] D[d4:2 d5:2 d6:2 d7:2 p3_8:2]`
|
||||
- face apexes (raw labels) `0000` → canonical `0000` · `A=012012121 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:0 d7:0 p3_8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u2:1] D[d4:1 d5:1 d6:1 d7:1 p3_8:1]`
|
||||
- face apexes (raw labels) `0000` → canonical `0000` · `A=012021212 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:0 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1] D[d4:2 d5:2 d6:2 d7:2 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0000`, realises `0000` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:0 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1] D[d4:1 d5:1 d6:1 d7:1 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0000`, realises `0000` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:0 d7:0 p3_8:1]`
|
||||
|
||||
## C08 — word=UUDUUDUDD bites=- face=root apexes=[d2,d5,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010120101 U[u0:2 u1:2 u3:0 u4:1 u6:2] D[d2:2 d5:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010210202 U[u0:2 u1:2 u3:0 u4:2 u6:1] D[d2:1 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012010202 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:1 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u3:1 u4:1 u6:1] D[d2:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010120101 U[u0:2 u1:2 u3:0 u4:1 u6:2] D[d2:2 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010210202 U[u0:2 u1:2 u3:0 u4:2 u6:1] D[d2:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012010202 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u3:1 u4:1 u6:1] D[d2:1 d5:1 d7:1 d8:1]`
|
||||
|
||||
## C09 — word=UUDUDUUDD bites=- face=root apexes=[d2,d4,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010101201 U[u0:2 u1:2 u3:2 u5:0 u6:1] D[d2:2 d4:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=010202102 U[u0:2 u1:2 u3:1 u5:0 u6:2] D[d2:1 d4:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020102 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u3:1 u5:1 u6:1] D[d2:1 d4:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u5:0 u6:1] D[d2:2 d4:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u5:0 u6:2] D[d2:1 d4:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u3:1 u5:1 u6:1] D[d2:1 d4:1 d7:1 d8:1]`
|
||||
|
||||
## C10 — word=UUDUDUDUD bites=- face=root apexes=[d2,d4,d6,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u3:1 u5:1 u7:1] D[d2:1 d4:1 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u3:1 u5:1 u7:1] D[d2:1 d4:1 d6:1 d8:1]`
|
||||
|
||||
## C11 — word=UUDUDDDDD bites=(2,4) face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012020101 U[u0:2 u1:0 u3:1] D[d5:2 d6:2 d7:2 d8:2 p2_4:1]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u3:1] D[d5:1 d6:1 d7:1 d8:1 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1] D[d5:2 d6:2 d7:2 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u3:1] D[d5:1 d6:1 d7:1 d8:1 p2_4:1]`
|
||||
|
||||
## C12 — word=UUDUDDDDD bites=(2,8) face=bite(2,8) apexes=[d4,d5,d6,d7]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u3:1] D[d4:1 d5:1 d6:1 d7:1 p2_8:1]`
|
||||
- face apexes (raw labels) `0000` → canonical `0000` · `A=012021212 U[u0:2 u1:0 u3:1] D[d4:0 d5:0 d6:0 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u3:1] D[d4:1 d5:1 d6:1 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0000`, realises `0000` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1] D[d4:0 d5:0 d6:0 d7:0 p2_8:1]`
|
||||
|
||||
## C13 — word=UUDDUDDDD bites=(3,5) face=root apexes=[d2,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u4:1] D[d2:1 d6:1 d7:1 d8:1 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u4:1] D[d2:1 d6:1 d7:1 d8:1 p3_5:1]`
|
||||
|
||||
## C14 — word=UUDDUDDDD bites=(2,8) face=bite(2,8) apexes=[d3,d5,d6,d7]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u4:1] D[d3:1 d5:1 d6:1 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u4:1] D[d3:1 d5:1 d6:1 d7:1 p2_8:1]`
|
||||
|
||||
## C15 — word=UUDDDUDDD bites=(4,6) face=root apexes=[d2,d3,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d7:1 d8:1 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d7:1 d8:1 p4_6:1]`
|
||||
|
||||
## C16 — word=UUDDDUDDD bites=(2,8) face=bite(2,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012020202 U[u0:2 u1:0 u5:1] D[d3:1 d4:1 d6:1 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012020202 U[u0:2 u1:0 u5:1] D[d3:1 d4:1 d6:1 d7:1 p2_8:1]`
|
||||
|
||||
## C17 — word=UDUDUDDDD bites=(3,5) face=root apexes=[d1,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d6:2 d7:2 d8:2 p3_5:0]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d6:2 d7:2 d8:2 p3_5:0]`
|
||||
|
||||
## C18 — word=UDUDUDDDD bites=(1,3) face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `2222` → canonical `0000` · `A=012120101 U[u0:2 u2:0 u4:1] D[d5:2 d6:2 d7:2 d8:2 p1_3:0]`
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012120202 U[u0:2 u2:0 u4:1] D[d5:1 d6:1 d7:1 d8:1 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `2222`, realises `0000` in some orientation · `A=012120101 U[u0:2 u2:0 u4:1] D[d5:2 d6:2 d7:2 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012120202 U[u0:2 u2:0 u4:1] D[d5:1 d6:1 d7:1 d8:1 p1_3:0]`
|
||||
|
||||
## C20 — word=UDUDDUDDD bites=(1,3) face=root apexes=[d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `1111` → canonical `0000` · `A=012120202 U[u0:2 u2:0 u5:1] D[d4:1 d6:1 d7:1 d8:1 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1111`, realises `0000` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d4:1 d6:1 d7:1 d8:1 p1_3:0]`
|
||||
|
||||
## C21 — word=UDUDDUDDD bites=(1,8) face=bite(1,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0000`:
|
||||
|
||||
- face apexes (raw labels) `0000` → canonical `0000` · `A=010212121 U[u0:2 u2:1 u5:0] D[d3:0 d4:0 d6:0 d7:0 p1_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0000`, realises `0000` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d3:0 d4:0 d6:0 d7:0 p1_8:2]`
|
||||
|
||||
|
||||
BIN
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@@ -1,234 +1,307 @@
|
||||
# Inner-face down-apex sequence `0011`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1.
|
||||
- Realised by **23** of 23 configs (M(T), inner face).
|
||||
- **108** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **181** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_0011.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUUUDDDD bites=- face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
10 colouring(s) with down-apex sequence `0011`:
|
||||
20 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010120102 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010210201 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012010201 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012020102 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012120102 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010120212 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010210121 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012010212 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012020121 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012120212 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C01 — word=UUUUDUDDD bites=- face=root apexes=[d4,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `0011`:
|
||||
10 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010120212 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010210121 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012120212 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUUDDUDD bites=- face=root apexes=[d4,d5,d7,d8]
|
||||
|
||||
15 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010121201 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=010121202 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:2 d5:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010212101 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=010212102 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:2 d5:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012012101 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012012102 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012021201 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012021202 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012121201 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012121202 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012012102 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012021201 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUUDUUDDD bites=- face=root apexes=[d3,d6,d7,d8]
|
||||
|
||||
7 colouring(s) with down-apex sequence `0011`:
|
||||
14 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010102102 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010201201 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010102 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012012102 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012021201 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012102102 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012012102 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012021201 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUUDUDUDD bites=- face=root apexes=[d3,d5,d7,d8]
|
||||
|
||||
8 colouring(s) with down-apex sequence `0011`:
|
||||
13 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010121201 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=010121202 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010212101 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=010212102 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010102 U[u0:2 u1:0 u2:1 u4:2 u6:2] D[d3:2 d5:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u2:1 u4:1 u6:1] D[d3:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012121201 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012121202 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u6:0] D[d3:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u4:2 u6:2] D[d3:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u4:1 u6:1] D[d3:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u6:0] D[d3:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UUUDUDDUD bites=- face=root apexes=[d3,d5,d6,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0011`:
|
||||
15 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=010121202 U[u0:2 u1:2 u2:2 u4:0 u7:1] D[d3:0 d5:0 d6:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010212101 U[u0:2 u1:2 u2:1 u4:0 u7:2] D[d3:0 d5:0 d6:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012121202 U[u0:2 u1:0 u2:0 u4:0 u7:1] D[d3:0 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u4:0 u7:1] D[d3:0 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u4:0 u7:2] D[d3:0 d5:0 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1 u4:2 u7:2] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1 u4:1 u7:1] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u4:0 u7:1] D[d3:0 d5:0 d6:1 d8:1]`
|
||||
|
||||
## C06 — word=UUUDDUUDD bites=- face=root apexes=[d3,d4,d7,d8]
|
||||
|
||||
13 colouring(s) with down-apex sequence `0011`:
|
||||
17 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010101202 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010121201 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=010121202 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010202101 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010212101 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=010212102 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010102 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010202 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020101 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012101202 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012121201 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012121202 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u5:0 u6:0] D[d3:2 d4:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u5:0 u6:0] D[d3:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
|
||||
## C07 — word=UUUDDDDDD bites=(3,8) face=bite(3,8) apexes=[d4,d5,d6,d7]
|
||||
|
||||
4 colouring(s) with down-apex sequence `0011`:
|
||||
8 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2200` → canonical `0011` · `A=012010121 U[u0:2 u1:0 u2:1] D[d4:2 d5:2 d6:0 d7:0 p3_8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012012101 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:2 d7:2 p3_8:2]`
|
||||
- face apexes (raw labels) `1100` → canonical `0011` · `A=012020212 U[u0:2 u1:0 u2:1] D[d4:1 d5:1 d6:0 d7:0 p3_8:1]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012021202 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:1 d7:1 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2200`, realises `0011` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1] D[d4:2 d5:2 d6:0 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1] D[d4:2 d5:1 d6:1 d7:2 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0110`, realises `0011` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1] D[d4:0 d5:1 d6:1 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:2 d7:2 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1] D[d4:1 d5:2 d6:2 d7:1 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1] D[d4:1 d5:1 d6:0 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0220`, realises `0011` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1] D[d4:0 d5:2 d6:2 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:1 d7:1 p3_8:1]`
|
||||
|
||||
## C08 — word=UUDUUDUDD bites=- face=root apexes=[d2,d5,d7,d8]
|
||||
|
||||
10 colouring(s) with down-apex sequence `0011`:
|
||||
13 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010120102 U[u0:2 u1:2 u3:0 u4:1 u6:2] D[d2:2 d5:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010210201 U[u0:2 u1:2 u3:0 u4:2 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012010201 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u3:1 u4:1 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012101201 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012101202 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012102101 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012102102 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012121201 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012121202 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010102121 U[u0:2 u1:2 u3:2 u4:1 u6:0] D[d2:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010120102 U[u0:2 u1:2 u3:0 u4:1 u6:2] D[d2:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010201212 U[u0:2 u1:2 u3:1 u4:2 u6:0] D[d2:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010210201 U[u0:2 u1:2 u3:0 u4:2 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012010201 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1 u4:1 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1 u4:0 u6:0] D[d2:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012101201 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012101202 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012102101 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012102102 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012121202 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
## C09 — word=UUDUDUUDD bites=- face=root apexes=[d2,d4,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `0011`:
|
||||
11 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010101202 U[u0:2 u1:2 u3:2 u5:0 u6:1] D[d2:2 d4:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010202101 U[u0:2 u1:2 u3:1 u5:0 u6:2] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020101 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u3:1 u5:1 u6:1] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012121201 U[u0:2 u1:0 u3:0 u5:0 u6:1] D[d2:0 d4:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012121202 U[u0:2 u1:0 u3:0 u5:0 u6:1] D[d2:0 d4:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u5:0 u6:1] D[d2:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u5:2 u6:1] D[d2:2 d4:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u5:0 u6:2] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u5:1 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u5:1 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1 u5:1 u6:1] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021012 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1 u5:0 u6:0] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u5:0 u6:1] D[d2:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012121202 U[u0:2 u1:0 u3:0 u5:0 u6:1] D[d2:0 d4:0 d7:1 d8:1]`
|
||||
|
||||
## C10 — word=UUDUDUDUD bites=- face=root apexes=[d2,d4,d6,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `0011`:
|
||||
10 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010101202 U[u0:2 u1:2 u3:2 u5:0 u7:1] D[d2:2 d4:2 d6:1 d8:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010202101 U[u0:2 u1:2 u3:1 u5:0 u7:2] D[d2:1 d4:1 d6:2 d8:2]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020101 U[u0:2 u1:0 u3:1 u5:2 u7:2] D[d2:1 d4:1 d6:2 d8:2]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012121202 U[u0:2 u1:0 u3:0 u5:0 u7:1] D[d2:0 d4:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u5:0 u7:1] D[d2:2 d4:2 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=010102021 U[u0:2 u1:2 u3:2 u5:1 u7:0] D[d2:2 d4:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=010120201 U[u0:2 u1:2 u3:0 u5:1 u7:2] D[d2:2 d4:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=010201012 U[u0:2 u1:2 u3:1 u5:2 u7:0] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u5:0 u7:2] D[d2:1 d4:1 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=010210102 U[u0:2 u1:2 u3:0 u5:2 u7:1] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=012010102 U[u0:2 u1:0 u3:2 u5:2 u7:1] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1 u5:2 u7:2] D[d2:1 d4:1 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1 u5:0 u7:0] D[d2:1 d4:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012121202 U[u0:2 u1:0 u3:0 u5:0 u7:1] D[d2:0 d4:0 d6:1 d8:1]`
|
||||
|
||||
## C11 — word=UUDUDDDDD bites=(2,4) face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
4 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012020102 U[u0:2 u1:0 u3:1] D[d5:2 d6:2 d7:1 d8:1 p2_4:1]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u3:1] D[d5:1 d6:1 d7:2 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d5:2 d6:2 d7:1 d8:1 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012020121 U[u0:2 u1:0 u3:1] D[d5:2 d6:0 d7:0 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1] D[d5:1 d6:1 d7:2 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d5:1 d6:0 d7:0 d8:1 p2_4:1]`
|
||||
|
||||
## C12 — word=UUDUDDDDD bites=(2,8) face=bite(2,8) apexes=[d4,d5,d6,d7]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
4 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1100` → canonical `0011` · `A=012020212 U[u0:2 u1:0 u3:1] D[d4:1 d5:1 d6:0 d7:0 p2_8:1]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012021202 U[u0:2 u1:0 u3:1] D[d4:0 d5:0 d6:1 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d4:1 d5:2 d6:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d4:1 d5:1 d6:0 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0220`, realises `0011` in some orientation · `A=012021012 U[u0:2 u1:0 u3:1] D[d4:0 d5:2 d6:2 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012021202 U[u0:2 u1:0 u3:1] D[d4:0 d5:0 d6:1 d7:1 p2_8:1]`
|
||||
|
||||
## C13 — word=UUDDUDDDD bites=(3,5) face=root apexes=[d2,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0011`:
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d6:1 d7:2 d8:2 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d6:1 d7:2 d8:2 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d6:0 d7:0 d8:1 p3_5:1]`
|
||||
|
||||
## C14 — word=UUDDUDDDD bites=(2,8) face=bite(2,8) apexes=[d3,d5,d6,d7]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0011`:
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1100` → canonical `0011` · `A=012020212 U[u0:2 u1:0 u4:1] D[d3:1 d5:1 d6:0 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0011` in some orientation · `A=012020102 U[u0:2 u1:0 u4:1] D[d3:1 d5:2 d6:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d3:1 d5:1 d6:0 d7:0 p2_8:1]`
|
||||
|
||||
## C15 — word=UUDDDUDDD bites=(4,6) face=root apexes=[d2,d3,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d7:2 d8:2 p4_6:1]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012120201 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d7:2 d8:2 p4_6:1]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d7:1 d8:1 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d7:2 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012120201 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d7:2 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d7:1 d8:1 p4_6:1]`
|
||||
|
||||
## C16 — word=UUDDDUDDD bites=(2,8) face=bite(2,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012010202 U[u0:2 u1:0 u5:1] D[d3:2 d4:2 d6:1 d7:1 p2_8:1]`
|
||||
- face apexes (raw labels) `2200` → canonical `0011` · `A=012010212 U[u0:2 u1:0 u5:1] D[d3:2 d4:2 d6:0 d7:0 p2_8:1]`
|
||||
- face apexes (raw labels) `1100` → canonical `0011` · `A=012020212 U[u0:2 u1:0 u5:1] D[d3:1 d4:1 d6:0 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012010202 U[u0:2 u1:0 u5:1] D[d3:2 d4:2 d6:1 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2200`, realises `0011` in some orientation · `A=012010212 U[u0:2 u1:0 u5:1] D[d3:2 d4:2 d6:0 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0011` in some orientation · `A=012020212 U[u0:2 u1:0 u5:1] D[d3:1 d4:1 d6:0 d7:0 p2_8:1]`
|
||||
|
||||
## C17 — word=UDUDUDDDD bites=(3,5) face=root apexes=[d1,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0011`:
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010212102 U[u0:2 u2:1 u4:0] D[d1:2 d6:2 d7:1 d8:1 p3_5:0]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010212102 U[u0:2 u2:1 u4:0] D[d1:2 d6:2 d7:1 d8:1 p3_5:0]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d6:0 d7:0 d8:2 p3_5:0]`
|
||||
|
||||
## C18 — word=UDUDUDDDD bites=(1,3) face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
4 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=012120102 U[u0:2 u2:0 u4:1] D[d5:2 d6:2 d7:1 d8:1 p1_3:0]`
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012120201 U[u0:2 u2:0 u4:1] D[d5:1 d6:1 d7:2 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=012120102 U[u0:2 u2:0 u4:1] D[d5:2 d6:2 d7:1 d8:1 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=012120121 U[u0:2 u2:0 u4:1] D[d5:2 d6:0 d7:0 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012120201 U[u0:2 u2:0 u4:1] D[d5:1 d6:1 d7:2 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012120212 U[u0:2 u2:0 u4:1] D[d5:1 d6:0 d7:0 d8:1 p1_3:0]`
|
||||
|
||||
## C19 — word=UDUDDUDDD bites=(4,6) face=root apexes=[d1,d3,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
3 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=012120201 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d7:2 d8:2 p4_6:1]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d7:1 d8:1 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0011` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d7:0 d8:2 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=012120201 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d7:2 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d7:1 d8:1 p4_6:1]`
|
||||
|
||||
## C20 — word=UDUDDUDDD bites=(1,3) face=root apexes=[d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0011`:
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=012120201 U[u0:2 u2:0 u5:1] D[d4:1 d6:1 d7:2 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=012120201 U[u0:2 u2:0 u5:1] D[d4:1 d6:1 d7:2 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0011` in some orientation · `A=012120212 U[u0:2 u2:0 u5:1] D[d4:1 d6:0 d7:0 d8:1 p1_3:0]`
|
||||
|
||||
## C21 — word=UDUDDUDDD bites=(1,8) face=bite(1,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `1122` → canonical `0011` · `A=010202101 U[u0:2 u2:1 u5:0] D[d3:1 d4:1 d6:2 d7:2 p1_8:2]`
|
||||
- face apexes (raw labels) `1100` → canonical `0011` · `A=010202121 U[u0:2 u2:1 u5:0] D[d3:1 d4:1 d6:0 d7:0 p1_8:2]`
|
||||
- face apexes (raw labels) `0022` → canonical `0011` · `A=010212101 U[u0:2 u2:1 u5:0] D[d3:0 d4:0 d6:2 d7:2 p1_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0011` in some orientation · `A=010202101 U[u0:2 u2:1 u5:0] D[d3:1 d4:1 d6:2 d7:2 p1_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0011` in some orientation · `A=010202121 U[u0:2 u2:1 u5:0] D[d3:1 d4:1 d6:0 d7:0 p1_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0011` in some orientation · `A=010212101 U[u0:2 u2:1 u5:0] D[d3:0 d4:0 d6:2 d7:2 p1_8:2]`
|
||||
|
||||
## C22 — word=UDDUDDUDD bites=(5,7) face=root apexes=[d1,d2,d4,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0011`:
|
||||
3 colouring(s) with down-apex sequence `0011`:
|
||||
|
||||
- face apexes (raw labels) `2211` → canonical `0011` · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d8:1 p5_7:1]`
|
||||
- face apexes (raw labels) `0011` → canonical `0011` · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0011` in some orientation · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0011` in some orientation · `A=010202121 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:1 d8:2 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0011` in some orientation · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d8:1 p5_7:1]`
|
||||
|
||||
|
||||
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|
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# Inner-face down-apex sequence `0101`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1.
|
||||
- Realised by **12** of 23 configs (M(T), inner face).
|
||||
- **53** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **53** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_0101.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
@@ -13,112 +13,112 @@ Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D
|
||||
|
||||
5 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=010121021 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=010212012 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012012012 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012021021 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012121021 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012012012 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012021021 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUUDUDUDD bites=- face=root apexes=[d3,d5,d7,d8]
|
||||
|
||||
9 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=010120121 U[u0:2 u1:2 u2:2 u4:1 u6:0] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=010120212 U[u0:2 u1:2 u2:2 u4:1 u6:0] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=010121021 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=010210121 U[u0:2 u1:2 u2:1 u4:2 u6:0] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=010210212 U[u0:2 u1:2 u2:1 u4:2 u6:0] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=010212012 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012120121 U[u0:2 u1:0 u2:0 u4:1 u6:0] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012120212 U[u0:2 u1:0 u2:0 u4:1 u6:0] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012121021 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u4:1 u6:0] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=010120212 U[u0:2 u1:2 u2:2 u4:1 u6:0] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=010210121 U[u0:2 u1:2 u2:1 u4:2 u6:0] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u4:2 u6:0] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u4:1 u6:0] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012120212 U[u0:2 u1:0 u2:0 u4:1 u6:0] D[d3:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UUUDUDDUD bites=- face=root apexes=[d3,d5,d6,d8]
|
||||
|
||||
11 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=010102012 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:1 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=010120121 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:0 d5:2 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=010120212 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:0 d5:1 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `1212` → canonical `0101` · `A=010201021 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=010210121 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:0 d5:2 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=010210212 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:0 d5:1 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=012012012 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:1 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1212` → canonical `0101` · `A=012021021 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=012102012 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:1 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012120121 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:0 d5:2 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012120212 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:0 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:0 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=010120212 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:0 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1212`, realises `0101` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=010210121 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:0 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:0 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=012012012 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1212`, realises `0101` in some orientation · `A=012021021 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:0 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012120212 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:0 d5:1 d6:0 d8:1]`
|
||||
|
||||
## C06 — word=UUUDDUUDD bites=- face=root apexes=[d3,d4,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=010120212 U[u0:2 u1:2 u2:2 u5:1 u6:0] D[d3:0 d4:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=010210121 U[u0:2 u1:2 u2:1 u5:2 u6:0] D[d3:0 d4:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012120212 U[u0:2 u1:0 u2:0 u5:1 u6:0] D[d3:0 d4:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=010120212 U[u0:2 u1:2 u2:2 u5:1 u6:0] D[d3:0 d4:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=010210121 U[u0:2 u1:2 u2:1 u5:2 u6:0] D[d3:0 d4:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012120212 U[u0:2 u1:0 u2:0 u5:1 u6:0] D[d3:0 d4:1 d7:0 d8:1]`
|
||||
|
||||
## C08 — word=UUDUUDUDD bites=- face=root apexes=[d2,d5,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012101021 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012102012 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012120121 U[u0:2 u1:0 u3:0 u4:1 u6:0] D[d2:0 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012120212 U[u0:2 u1:0 u3:0 u4:1 u6:0] D[d2:0 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012121021 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012101021 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012102012 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012120121 U[u0:2 u1:0 u3:0 u4:1 u6:0] D[d2:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012120212 U[u0:2 u1:0 u3:0 u4:1 u6:0] D[d2:0 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012121021 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
## C09 — word=UUDUDUUDD bites=- face=root apexes=[d2,d4,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012101021 U[u0:2 u1:0 u3:2 u5:2 u6:1] D[d2:0 d4:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012102012 U[u0:2 u1:0 u3:2 u5:1 u6:2] D[d2:0 d4:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012120212 U[u0:2 u1:0 u3:0 u5:1 u6:0] D[d2:0 d4:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012101021 U[u0:2 u1:0 u3:2 u5:2 u6:1] D[d2:0 d4:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012102012 U[u0:2 u1:0 u3:2 u5:1 u6:2] D[d2:0 d4:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012120212 U[u0:2 u1:0 u3:0 u5:1 u6:0] D[d2:0 d4:1 d7:0 d8:1]`
|
||||
|
||||
## C10 — word=UUDUDUDUD bites=- face=root apexes=[d2,d4,d6,d8]
|
||||
|
||||
8 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=010102012 U[u0:2 u1:2 u3:2 u5:1 u7:0] D[d2:2 d4:1 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=010102102 U[u0:2 u1:2 u3:2 u5:0 u7:1] D[d2:2 d4:1 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=010120102 U[u0:2 u1:2 u3:0 u5:2 u7:1] D[d2:2 d4:1 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1212` → canonical `0101` · `A=010201021 U[u0:2 u1:2 u3:1 u5:2 u7:0] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `1212` → canonical `0101` · `A=010201201 U[u0:2 u1:2 u3:1 u5:0 u7:2] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `1212` → canonical `0101` · `A=010210201 U[u0:2 u1:2 u3:0 u5:1 u7:2] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `1212` → canonical `0101` · `A=012010201 U[u0:2 u1:0 u3:2 u5:1 u7:2] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012120212 U[u0:2 u1:0 u3:0 u5:1 u7:0] D[d2:0 d4:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=010102012 U[u0:2 u1:2 u3:2 u5:1 u7:0] D[d2:2 d4:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=010102102 U[u0:2 u1:2 u3:2 u5:0 u7:1] D[d2:2 d4:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=010120102 U[u0:2 u1:2 u3:0 u5:2 u7:1] D[d2:2 d4:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1212`, realises `0101` in some orientation · `A=010201021 U[u0:2 u1:2 u3:1 u5:2 u7:0] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1212`, realises `0101` in some orientation · `A=010201201 U[u0:2 u1:2 u3:1 u5:0 u7:2] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1212`, realises `0101` in some orientation · `A=010210201 U[u0:2 u1:2 u3:0 u5:1 u7:2] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1212`, realises `0101` in some orientation · `A=012010201 U[u0:2 u1:0 u3:2 u5:1 u7:2] D[d2:1 d4:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012120212 U[u0:2 u1:0 u3:0 u5:1 u7:0] D[d2:0 d4:1 d6:0 d8:1]`
|
||||
|
||||
## C15 — word=UUDDDUDDD bites=(4,6) face=root apexes=[d2,d3,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012102021 U[u0:2 u1:0 u5:1] D[d2:0 d3:2 d7:0 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012102021 U[u0:2 u1:0 u5:1] D[d2:0 d3:2 d7:0 d8:2 p4_6:1]`
|
||||
|
||||
## C16 — word=UUDDDUDDD bites=(2,8) face=bite(2,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `2020` → canonical `0101` · `A=012012012 U[u0:2 u1:0 u5:1] D[d3:2 d4:0 d6:2 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2020`, realises `0101` in some orientation · `A=012012012 U[u0:2 u1:0 u5:1] D[d3:2 d4:0 d6:2 d7:0 p2_8:1]`
|
||||
|
||||
## C19 — word=UDUDDUDDD bites=(4,6) face=root apexes=[d1,d3,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d7:0 d8:2 p4_6:0]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d7:0 d8:1 p4_6:0]`
|
||||
- face apexes (raw labels) `0202` → canonical `0101` · `A=012102021 U[u0:2 u2:0 u5:1] D[d1:0 d3:2 d7:0 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d7:0 d8:2 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d7:0 d8:1 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `0202`, realises `0101` in some orientation · `A=012102021 U[u0:2 u2:0 u5:1] D[d1:0 d3:2 d7:0 d8:2 p4_6:1]`
|
||||
|
||||
## C21 — word=UDUDDUDDD bites=(1,8) face=bite(1,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `1212` → canonical `0101` · `A=010201201 U[u0:2 u2:1 u5:0] D[d3:1 d4:2 d6:1 d7:2 p1_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1212`, realises `0101` in some orientation · `A=010201201 U[u0:2 u2:1 u5:0] D[d3:1 d4:2 d6:1 d7:2 p1_8:2]`
|
||||
|
||||
## C22 — word=UDDUDDUDD bites=(5,7) face=root apexes=[d1,d2,d4,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0101`:
|
||||
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=010201212 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:2 d8:1 p5_7:0]`
|
||||
- face apexes (raw labels) `2121` → canonical `0101` · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d8:1 p5_7:1]`
|
||||
- face apexes (raw labels) `0101` → canonical `0101` · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=010201212 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:2 d8:1 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `2121`, realises `0101` in some orientation · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `0101`, realises `0101` in some orientation · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d8:1 p5_7:0]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `0110`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1.
|
||||
- Realised by **19** of 23 configs (M(T), inner face).
|
||||
- **73** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **23** of 23 configs (M(T), inner face).
|
||||
- **181** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_0110.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUUUDDDD bites=- face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
10 colouring(s) with down-apex sequence `0110`:
|
||||
20 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010120121 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010120212 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010210121 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010210212 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012010121 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012010212 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012020121 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012020212 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012120121 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012120212 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010120212 U[u0:2 u1:2 u2:2 u3:0 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010210121 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u3:0 u4:2] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012010212 U[u0:2 u1:0 u2:1 u3:2 u4:2] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012020121 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1 u3:1 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012120212 U[u0:2 u1:0 u2:0 u3:0 u4:1] D[d5:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C01 — word=UUUUDUDDD bites=- face=root apexes=[d4,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `0110`:
|
||||
10 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010120212 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010210121 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012010121 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012020212 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012120212 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010120212 U[u0:2 u1:2 u2:2 u3:0 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010210121 U[u0:2 u1:2 u2:1 u3:0 u5:2] D[d4:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1 u3:2 u5:2] D[d4:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1 u3:1 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012120212 U[u0:2 u1:0 u2:0 u3:0 u5:1] D[d4:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUUDDUDD bites=- face=root apexes=[d4,d5,d7,d8]
|
||||
|
||||
15 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010120201 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u3:0 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010210102 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u3:0 u6:2] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012012102 U[u0:2 u1:0 u2:1 u3:2 u6:2] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012021201 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1 u3:1 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012120201 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u3:0 u6:1] D[d4:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUUDUUDDD bites=- face=root apexes=[d3,d6,d7,d8]
|
||||
|
||||
7 colouring(s) with down-apex sequence `0110`:
|
||||
14 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012010121 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012020212 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u5:0] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1 u4:2 u5:2] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012012102 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1 u4:1 u5:1] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012021201 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u5:0] D[d3:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u5:0] D[d3:2 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUUDUDUDD bites=- face=root apexes=[d3,d5,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `0110`:
|
||||
13 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u6:0] D[d3:1 d5:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u6:0] D[d3:1 d5:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u4:0 u6:1] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u6:0] D[d3:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u4:0 u6:2] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u4:2 u6:2] D[d3:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u4:1 u6:1] D[d3:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u6:0] D[d3:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u6:0] D[d3:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u4:0 u6:1] D[d3:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UUUDUDDUD bites=- face=root apexes=[d3,d5,d6,d8]
|
||||
|
||||
12 colouring(s) with down-apex sequence `0110`:
|
||||
15 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=010102021 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=010201012 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:0 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=012010201 U[u0:2 u1:0 u2:1 u4:2 u7:2] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=012012021 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=012020102 U[u0:2 u1:0 u2:1 u4:1 u7:1] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=012021012 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:0 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=012102021 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u4:1 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u4:0 u7:1] D[d3:0 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u4:2 u7:0] D[d3:1 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u4:0 u7:2] D[d3:0 d5:0 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1 u4:2 u7:2] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1 u4:1 u7:1] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u4:0 u7:0] D[d3:1 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u4:1 u7:0] D[d3:2 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u4:0 u7:1] D[d3:0 d5:0 d6:1 d8:1]`
|
||||
|
||||
## C06 — word=UUUDDUUDD bites=- face=root apexes=[d3,d4,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `0110`:
|
||||
17 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012012021 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012012121 U[u0:2 u1:0 u2:1 u5:0 u6:0] D[d3:2 d4:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021012 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021212 U[u0:2 u1:0 u2:1 u5:0 u6:0] D[d3:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010121201 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=010121202 U[u0:2 u1:2 u2:2 u5:0 u6:1] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010212101 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=010212102 U[u0:2 u1:2 u2:1 u5:0 u6:2] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:2 d4:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1 u5:0 u6:0] D[d3:2 d4:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1 u5:1 u6:1] D[d3:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1 u5:2 u6:2] D[d3:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1 u5:0 u6:0] D[d3:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012121201 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012121202 U[u0:2 u1:0 u2:0 u5:0 u6:1] D[d3:0 d4:0 d7:1 d8:1]`
|
||||
|
||||
## C07 — word=UUUDDDDDD bites=(3,8) face=bite(3,8) apexes=[d4,d5,d6,d7]
|
||||
|
||||
4 colouring(s) with down-apex sequence `0110`:
|
||||
8 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=012010201 U[u0:2 u1:0 u2:1] D[d4:2 d5:1 d6:1 d7:2 p3_8:2]`
|
||||
- face apexes (raw labels) `0110` → canonical `0110` · `A=012012021 U[u0:2 u1:0 u2:1] D[d4:0 d5:1 d6:1 d7:0 p3_8:2]`
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=012020102 U[u0:2 u1:0 u2:1] D[d4:1 d5:2 d6:2 d7:1 p3_8:1]`
|
||||
- face apexes (raw labels) `0220` → canonical `0110` · `A=012021012 U[u0:2 u1:0 u2:1] D[d4:0 d5:2 d6:2 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2200`, realises `0110` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1] D[d4:2 d5:2 d6:0 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1] D[d4:2 d5:1 d6:1 d7:2 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0110`, realises `0110` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1] D[d4:0 d5:1 d6:1 d7:0 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:2 d7:2 p3_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1] D[d4:1 d5:2 d6:2 d7:1 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1] D[d4:1 d5:1 d6:0 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0220`, realises `0110` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1] D[d4:0 d5:2 d6:2 d7:0 p3_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1] D[d4:0 d5:0 d6:1 d7:1 p3_8:1]`
|
||||
|
||||
## C08 — word=UUDUUDUDD bites=- face=root apexes=[d2,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0110`:
|
||||
13 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010102121 U[u0:2 u1:2 u3:2 u4:1 u6:0] D[d2:2 d5:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010201212 U[u0:2 u1:2 u3:1 u4:2 u6:0] D[d2:1 d5:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021212 U[u0:2 u1:0 u3:1 u4:0 u6:0] D[d2:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010102121 U[u0:2 u1:2 u3:2 u4:1 u6:0] D[d2:2 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010120102 U[u0:2 u1:2 u3:0 u4:1 u6:2] D[d2:2 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010201212 U[u0:2 u1:2 u3:1 u4:2 u6:0] D[d2:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010210201 U[u0:2 u1:2 u3:0 u4:2 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012010201 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1 u4:1 u6:1] D[d2:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1 u4:0 u6:0] D[d2:1 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012101201 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012101202 U[u0:2 u1:0 u3:2 u4:2 u6:1] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012102101 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012102102 U[u0:2 u1:0 u3:2 u4:1 u6:2] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012121202 U[u0:2 u1:0 u3:0 u4:0 u6:1] D[d2:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
## C09 — word=UUDUDUUDD bites=- face=root apexes=[d2,d4,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `0110`:
|
||||
11 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010121021 U[u0:2 u1:2 u3:0 u5:2 u6:1] D[d2:2 d4:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=010212012 U[u0:2 u1:2 u3:0 u5:1 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012012012 U[u0:2 u1:0 u3:2 u5:1 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021012 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021212 U[u0:2 u1:0 u3:1 u5:0 u6:0] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u5:0 u6:1] D[d2:2 d4:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u5:2 u6:1] D[d2:2 d4:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u5:0 u6:2] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u5:1 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u5:1 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1 u5:1 u6:1] D[d2:1 d4:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021012 U[u0:2 u1:0 u3:1 u5:2 u6:2] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1 u5:0 u6:0] D[d2:1 d4:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u5:0 u6:1] D[d2:0 d4:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012121202 U[u0:2 u1:0 u3:0 u5:0 u6:1] D[d2:0 d4:0 d7:1 d8:1]`
|
||||
|
||||
## C10 — word=UUDUDUDUD bites=- face=root apexes=[d2,d4,d6,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `0110`:
|
||||
10 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=010102021 U[u0:2 u1:2 u3:2 u5:1 u7:0] D[d2:2 d4:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=010120201 U[u0:2 u1:2 u3:0 u5:1 u7:2] D[d2:2 d4:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=010201012 U[u0:2 u1:2 u3:1 u5:2 u7:0] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=010210102 U[u0:2 u1:2 u3:0 u5:2 u7:1] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=012010102 U[u0:2 u1:0 u3:2 u5:2 u7:1] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012021212 U[u0:2 u1:0 u3:1 u5:0 u7:0] D[d2:1 d4:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u5:0 u7:1] D[d2:2 d4:2 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=010102021 U[u0:2 u1:2 u3:2 u5:1 u7:0] D[d2:2 d4:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=010120201 U[u0:2 u1:2 u3:0 u5:1 u7:2] D[d2:2 d4:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=010201012 U[u0:2 u1:2 u3:1 u5:2 u7:0] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u5:0 u7:2] D[d2:1 d4:1 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=010210102 U[u0:2 u1:2 u3:0 u5:2 u7:1] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=012010102 U[u0:2 u1:0 u3:2 u5:2 u7:1] D[d2:1 d4:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1 u5:2 u7:2] D[d2:1 d4:1 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1 u5:0 u7:0] D[d2:1 d4:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012121202 U[u0:2 u1:0 u3:0 u5:0 u7:1] D[d2:0 d4:0 d6:1 d8:1]`
|
||||
|
||||
## C11 — word=UUDUDDDDD bites=(2,4) face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0110`:
|
||||
4 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012020121 U[u0:2 u1:0 u3:1] D[d5:2 d6:0 d7:0 d8:2 p2_4:1]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012020212 U[u0:2 u1:0 u3:1] D[d5:1 d6:0 d7:0 d8:1 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d5:2 d6:2 d7:1 d8:1 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012020121 U[u0:2 u1:0 u3:1] D[d5:2 d6:0 d7:0 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1] D[d5:1 d6:1 d7:2 d8:2 p2_4:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d5:1 d6:0 d7:0 d8:1 p2_4:1]`
|
||||
|
||||
## C12 — word=UUDUDDDDD bites=(2,8) face=bite(2,8) apexes=[d4,d5,d6,d7]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0110`:
|
||||
4 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=012020102 U[u0:2 u1:0 u3:1] D[d4:1 d5:2 d6:2 d7:1 p2_8:1]`
|
||||
- face apexes (raw labels) `0220` → canonical `0110` · `A=012021012 U[u0:2 u1:0 u3:1] D[d4:0 d5:2 d6:2 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d4:1 d5:2 d6:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d4:1 d5:1 d6:0 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0220`, realises `0110` in some orientation · `A=012021012 U[u0:2 u1:0 u3:1] D[d4:0 d5:2 d6:2 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012021202 U[u0:2 u1:0 u3:1] D[d4:0 d5:0 d6:1 d7:1 p2_8:1]`
|
||||
|
||||
## C13 — word=UUDDUDDDD bites=(3,5) face=root apexes=[d2,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0110`:
|
||||
2 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d6:0 d7:0 d8:1 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d6:1 d7:2 d8:2 p3_5:1]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d6:0 d7:0 d8:1 p3_5:1]`
|
||||
|
||||
## C14 — word=UUDDUDDDD bites=(2,8) face=bite(2,8) apexes=[d3,d5,d6,d7]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0110`:
|
||||
2 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `1221` → canonical `0110` · `A=012020102 U[u0:2 u1:0 u4:1] D[d3:1 d5:2 d6:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1221`, realises `0110` in some orientation · `A=012020102 U[u0:2 u1:0 u4:1] D[d3:1 d5:2 d6:2 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d3:1 d5:1 d6:0 d7:0 p2_8:1]`
|
||||
|
||||
## C15 — word=UUDDDUDDD bites=(4,6) face=root apexes=[d2,d3,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d7:2 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012120201 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d7:2 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d7:1 d8:1 p4_6:1]`
|
||||
|
||||
## C16 — word=UUDDDUDDD bites=(2,8) face=bite(2,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012010202 U[u0:2 u1:0 u5:1] D[d3:2 d4:2 d6:1 d7:1 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `2200`, realises `0110` in some orientation · `A=012010212 U[u0:2 u1:0 u5:1] D[d3:2 d4:2 d6:0 d7:0 p2_8:1]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0110` in some orientation · `A=012020212 U[u0:2 u1:0 u5:1] D[d3:1 d4:1 d6:0 d7:0 p2_8:1]`
|
||||
|
||||
## C17 — word=UDUDUDDDD bites=(3,5) face=root apexes=[d1,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0110`:
|
||||
2 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d6:0 d7:0 d8:2 p3_5:0]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010212102 U[u0:2 u2:1 u4:0] D[d1:2 d6:2 d7:1 d8:1 p3_5:0]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d6:0 d7:0 d8:2 p3_5:0]`
|
||||
|
||||
## C18 — word=UDUDUDDDD bites=(1,3) face=root apexes=[d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `0110`:
|
||||
4 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=012120121 U[u0:2 u2:0 u4:1] D[d5:2 d6:0 d7:0 d8:2 p1_3:0]`
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012120212 U[u0:2 u2:0 u4:1] D[d5:1 d6:0 d7:0 d8:1 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=012120102 U[u0:2 u2:0 u4:1] D[d5:2 d6:2 d7:1 d8:1 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=012120121 U[u0:2 u2:0 u4:1] D[d5:2 d6:0 d7:0 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012120201 U[u0:2 u2:0 u4:1] D[d5:1 d6:1 d7:2 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012120212 U[u0:2 u2:0 u4:1] D[d5:1 d6:0 d7:0 d8:1 p1_3:0]`
|
||||
|
||||
## C19 — word=UDUDDUDDD bites=(4,6) face=root apexes=[d1,d3,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0110`:
|
||||
3 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2002` → canonical `0110` · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d7:0 d8:2 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `2002`, realises `0110` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d7:0 d8:2 p4_6:0]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=012120201 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d7:2 d8:2 p4_6:1]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d7:1 d8:1 p4_6:1]`
|
||||
|
||||
## C20 — word=UDUDDUDDD bites=(1,3) face=root apexes=[d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0110`:
|
||||
2 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `1001` → canonical `0110` · `A=012120212 U[u0:2 u2:0 u5:1] D[d4:1 d6:0 d7:0 d8:1 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=012120201 U[u0:2 u2:0 u5:1] D[d4:1 d6:1 d7:2 d8:2 p1_3:0]`
|
||||
- face apex colours (canonical-rep edge order) `1001`, realises `0110` in some orientation · `A=012120212 U[u0:2 u2:0 u5:1] D[d4:1 d6:0 d7:0 d8:1 p1_3:0]`
|
||||
|
||||
## C21 — word=UDUDDUDDD bites=(1,8) face=bite(1,8) apexes=[d3,d4,d6,d7]
|
||||
|
||||
3 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `1122`, realises `0110` in some orientation · `A=010202101 U[u0:2 u2:1 u5:0] D[d3:1 d4:1 d6:2 d7:2 p1_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `1100`, realises `0110` in some orientation · `A=010202121 U[u0:2 u2:1 u5:0] D[d3:1 d4:1 d6:0 d7:0 p1_8:2]`
|
||||
- face apex colours (canonical-rep edge order) `0022`, realises `0110` in some orientation · `A=010212101 U[u0:2 u2:1 u5:0] D[d3:0 d4:0 d6:2 d7:2 p1_8:2]`
|
||||
|
||||
## C22 — word=UDDUDDUDD bites=(5,7) face=root apexes=[d1,d2,d4,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `0110`:
|
||||
3 colouring(s) with down-apex sequence `0110`:
|
||||
|
||||
- face apexes (raw labels) `2112` → canonical `0110` · `A=010202121 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:1 d8:2 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `2211`, realises `0110` in some orientation · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d8:1 p5_7:1]`
|
||||
- face apex colours (canonical-rep edge order) `2112`, realises `0110` in some orientation · `A=010202121 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:1 d8:2 p5_7:0]`
|
||||
- face apex colours (canonical-rep edge order) `0011`, realises `0110` in some orientation · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d8:1 p5_7:1]`
|
||||
|
||||
|
||||
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+9
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@@ -1,6 +1,6 @@
|
||||
# Inner-face singleton-down-apex sequences of Kempe-balanced colourings (n=9, m=4)
|
||||
|
||||
Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedral class) that has an inner non-tooth face holding exactly 4 singleton down-tooth apexes: **23 configs (M(T), inner face)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the down-apex colour sequence in increasing annular-edge order, and reduce it modulo colour permutation (NOT dihedral symmetry).
|
||||
Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedral class) that has an inner non-tooth face holding exactly 4 singleton down-tooth apexes: **23 configs (M(T), inner face)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the down-apex colour sequence in cyclic order off the un-deduped census (every cyclic orientation of each colouring), and reduce it modulo colour permutation (NOT dihedral symmetry). Reading off the census makes the recorded vocabulary orientation-honest; see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Total Kempe-balanced colourings (mod colour permutation): **298**.
|
||||
- Distinct canonical down-apex sequences overall: **4**.
|
||||
@@ -10,21 +10,20 @@ Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedr
|
||||
| sequence | colour multiset | #configs realising | #colourings |
|
||||
|---|---|---|---|
|
||||
| `0000` | 4 | 21 | 64 |
|
||||
| `0011` | 2+2 | 23 | 108 |
|
||||
| `0011` | 2+2 | 23 | 181 |
|
||||
| `0101` | 2+2 | 12 | 53 |
|
||||
| `0110` | 2+2 | 19 | 73 |
|
||||
| `0110` | 2+2 | 23 | 181 |
|
||||
|
||||
Note: every realised sequence has its three colour-counts of **equal parity** — exactly the Kempe-parity constraint on the inner face (each colour pair meets its singleton down apexes an even number of times). With m = 4 apexes (m is even) every count must be **even**, so the only admissible colour multisets are 2+2, 4.
|
||||
|
||||
## Step 4 — grouping configs by their set of unique down-apex sequences
|
||||
|
||||
The 23 configs fall into **4** groups by the set of canonical down-apex sequences they realise:
|
||||
The 23 configs fall into **3** groups by the set of canonical down-apex sequences they realise:
|
||||
|
||||
| #configs | set of down-apex sequences | config ids |
|
||||
|---|---|---|
|
||||
| 11 | { `0000`, `0011`, `0110` } | C00, C01, C03, C07, C11, C12, C13, C14, C17, C18, C20 |
|
||||
| 6 | { `0000`, `0011`, `0101`, `0110` } | C04, C05, C06, C08, C09, C10 |
|
||||
| 4 | { `0000`, `0011`, `0101` } | C02, C15, C16, C21 |
|
||||
| 10 | { `0000`, `0011`, `0101`, `0110` } | C02, C04, C05, C06, C08, C09, C10, C15, C16, C21 |
|
||||
| 2 | { `0011`, `0101`, `0110` } | C19, C22 |
|
||||
|
||||
## Config atlas (ids)
|
||||
@@ -33,7 +32,7 @@ The 23 configs fall into **4** groups by the set of canonical down-apex sequence
|
||||
|---|---|---|---|
|
||||
| C00 | word=UUUUUDDDD bites=- face=root apexes=[d5,d6,d7,d8] | 30 | { `0000`, `0011`, `0110` } |
|
||||
| C01 | word=UUUUDUDDD bites=- face=root apexes=[d4,d6,d7,d8] | 15 | { `0000`, `0011`, `0110` } |
|
||||
| C02 | word=UUUUDDUDD bites=- face=root apexes=[d4,d5,d7,d8] | 25 | { `0000`, `0011`, `0101` } |
|
||||
| C02 | word=UUUUDDUDD bites=- face=root apexes=[d4,d5,d7,d8] | 25 | { `0000`, `0011`, `0101`, `0110` } |
|
||||
| C03 | word=UUUDUUDDD bites=- face=root apexes=[d3,d6,d7,d8] | 21 | { `0000`, `0011`, `0110` } |
|
||||
| C04 | word=UUUDUDUDD bites=- face=root apexes=[d3,d5,d7,d8] | 24 | { `0000`, `0011`, `0101`, `0110` } |
|
||||
| C05 | word=UUUDUDDUD bites=- face=root apexes=[d3,d5,d6,d8] | 28 | { `0000`, `0011`, `0101`, `0110` } |
|
||||
@@ -46,13 +45,13 @@ The 23 configs fall into **4** groups by the set of canonical down-apex sequence
|
||||
| C12 | word=UUDUDDDDD bites=(2,8) face=bite(2,8) apexes=[d4,d5,d6,d7] | 6 | { `0000`, `0011`, `0110` } |
|
||||
| C13 | word=UUDDUDDDD bites=(3,5) face=root apexes=[d2,d6,d7,d8] | 3 | { `0000`, `0011`, `0110` } |
|
||||
| C14 | word=UUDDUDDDD bites=(2,8) face=bite(2,8) apexes=[d3,d5,d6,d7] | 3 | { `0000`, `0011`, `0110` } |
|
||||
| C15 | word=UUDDDUDDD bites=(4,6) face=root apexes=[d2,d3,d7,d8] | 5 | { `0000`, `0011`, `0101` } |
|
||||
| C16 | word=UUDDDUDDD bites=(2,8) face=bite(2,8) apexes=[d3,d4,d6,d7] | 5 | { `0000`, `0011`, `0101` } |
|
||||
| C15 | word=UUDDDUDDD bites=(4,6) face=root apexes=[d2,d3,d7,d8] | 5 | { `0000`, `0011`, `0101`, `0110` } |
|
||||
| C16 | word=UUDDDUDDD bites=(2,8) face=bite(2,8) apexes=[d3,d4,d6,d7] | 5 | { `0000`, `0011`, `0101`, `0110` } |
|
||||
| C17 | word=UDUDUDDDD bites=(3,5) face=root apexes=[d1,d6,d7,d8] | 3 | { `0000`, `0011`, `0110` } |
|
||||
| C18 | word=UDUDUDDDD bites=(1,3) face=root apexes=[d5,d6,d7,d8] | 6 | { `0000`, `0011`, `0110` } |
|
||||
| C19 | word=UDUDDUDDD bites=(4,6) face=root apexes=[d1,d3,d7,d8] | 6 | { `0011`, `0101`, `0110` } |
|
||||
| C20 | word=UDUDDUDDD bites=(1,3) face=root apexes=[d4,d6,d7,d8] | 3 | { `0000`, `0011`, `0110` } |
|
||||
| C21 | word=UDUDDUDDD bites=(1,8) face=bite(1,8) apexes=[d3,d4,d6,d7] | 5 | { `0000`, `0011`, `0101` } |
|
||||
| C21 | word=UDUDDUDDD bites=(1,8) face=bite(1,8) apexes=[d3,d4,d6,d7] | 5 | { `0000`, `0011`, `0101`, `0110` } |
|
||||
| C22 | word=UDDUDDUDD bites=(5,7) face=root apexes=[d1,d2,d4,d8] | 6 | { `0011`, `0101`, `0110` } |
|
||||
|
||||
## Per-sequence notes
|
||||
|
||||
+173
-42
@@ -1,91 +1,222 @@
|
||||
# Inner-face down-apex sequence `00012`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
|
||||
- Realised by **10** of 10 configs (M(T), inner face).
|
||||
- **30** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **161** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_00012.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUUDDDDD bites=- face=root apexes=[d4,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `00012`:
|
||||
30 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010102021 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010201012 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=012101012 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=012102021 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010102101 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010201202 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=012102101 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C01 — word=UUUDUDDDD bites=- face=root apexes=[d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `00012`:
|
||||
15 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `00012`:
|
||||
9 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00012` in some orientation · `A=010120101 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00012` in some orientation · `A=010210202 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00012` in some orientation · `A=012120101 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C03 — word=UUDUUDDDD bites=- face=root apexes=[d2,d5,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `00012`:
|
||||
25 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010101212 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010202121 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `00012`:
|
||||
16 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00012` in some orientation · `A=012101202 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00012` in some orientation · `A=012102101 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00012` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `00012`:
|
||||
8 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:2 d5:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00012` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `00012` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00012` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `00012`:
|
||||
12 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `00012` → canonical `00012` · `A=012121201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:0 d5:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22012`, realises `00012` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:2 d5:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00012` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `00012` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11021`, realises `00012` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:1 d5:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02221`, realises `00012` in some orientation · `A=012101012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `00012` in some orientation · `A=012102021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00012` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `00012` in some orientation · `A=012120201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00012`, realises `00012` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:0 d5:0 d6:1 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `00012`:
|
||||
23 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010101021 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010121201 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010121202 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010202012 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010212101 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010212102 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00012` in some orientation · `A=012101202 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `00012`:
|
||||
12 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u1:2 u4:2 u6:2] D[d2:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11102` → canonical `00012` · `A=010202021 U[u0:2 u1:2 u4:1 u6:1] D[d2:1 d3:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u6:2] D[d2:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00012` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u6:1] D[d2:1 d3:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00012` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00012` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00012` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `00012` in some orientation · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00012` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `00012`:
|
||||
11 colouring(s) with down-apex sequence `00012`:
|
||||
|
||||
- face apexes (raw labels) `22201` → canonical `00012` · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00012` in some orientation · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00012` in some orientation · `A=010102021 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010120201 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00012` in some orientation · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00012` in some orientation · `A=010201201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00012` in some orientation · `A=010202101 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00012` in some orientation · `A=010210201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00012` in some orientation · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00012` in some orientation · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00012` in some orientation · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `00102`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
|
||||
- Realised by **6** of 10 configs (M(T), inner face).
|
||||
- **13** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 10 configs (M(T), inner face).
|
||||
- **68** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_00102.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `00102`:
|
||||
12 colouring(s) with down-apex sequence `00102`:
|
||||
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=010121012 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `00102` → canonical `00102` · `A=010121021 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=010212012 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `00102` → canonical `00102` · `A=010212021 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=012121012 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `00102` → canonical `00102` · `A=012121021 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `00102` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `00102` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `00102` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `00102` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `00102` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `00102` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `00102` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `00102` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `00102` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `00102`:
|
||||
8 colouring(s) with down-apex sequence `00102`:
|
||||
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `00102` → canonical `00102` · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `00102` in some orientation · `A=012101201 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `00102` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `00102` in some orientation · `A=012102102 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `00102` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `00102` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `00102` in some orientation · `A=012120121 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `00102` in some orientation · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `00102`:
|
||||
14 colouring(s) with down-apex sequence `00102`:
|
||||
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:0 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `00102` in some orientation · `A=010102012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `00102` in some orientation · `A=010102102 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `00102` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `00102` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `00102` in some orientation · `A=010201021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `00102` in some orientation · `A=010201201 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `00102` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `00102` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `00102` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `00102` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `00102` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `00102` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `00102` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
16 colouring(s) with down-apex sequence `00102`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `00102` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `00102` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20221`, realises `00102` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20212`, realises `00102` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `00102` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `00102` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `00102` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `00102` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `00102` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `00102` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `00102` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `00102` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02212`, realises `00102` in some orientation · `A=012101021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `00102` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01121`, realises `00102` in some orientation · `A=012102012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `00102` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:0 d6:0 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `00102`:
|
||||
4 colouring(s) with down-apex sequence `00102`:
|
||||
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=012121012 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `00102` → canonical `00102` · `A=012121021 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `00102` in some orientation · `A=012101201 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `00102` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `00102` in some orientation · `A=012121021 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `00102`:
|
||||
6 colouring(s) with down-apex sequence `00102`:
|
||||
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=012121012 U[u0:2 u1:0 u4:0 u6:2] D[d2:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `00102` in some orientation · `A=012010121 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `00102` in some orientation · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `00102` in some orientation · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `00102` in some orientation · `A=012012101 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `00102` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u6:2] D[d2:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `00102`:
|
||||
8 colouring(s) with down-apex sequence `00102`:
|
||||
|
||||
- face apexes (raw labels) `00201` → canonical `00102` · `A=012121012 U[u0:2 u2:0 u4:0 u6:2] D[d1:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `00102` in some orientation · `A=010201021 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `00102` in some orientation · `A=010201202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `00102` in some orientation · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `00102` in some orientation · `A=010202102 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `00102` in some orientation · `A=012010201 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `00102` in some orientation · `A=012020102 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `00102` in some orientation · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `00102` in some orientation · `A=012121012 U[u0:2 u2:0 u4:0 u6:2] D[d1:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
|
||||
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||||
# Inner-face down-apex sequence `00120`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
|
||||
- Realised by **9** of 10 configs (M(T), inner face).
|
||||
- **30** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **10** of 10 configs (M(T), inner face).
|
||||
- **161** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_00120.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUUDDDDD bites=- face=root apexes=[d4,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `00120`:
|
||||
30 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010102101 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010201202 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=012102101 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C01 — word=UUUDUDDDD bites=- face=root apexes=[d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `00120`:
|
||||
15 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `00120`:
|
||||
9 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00120` in some orientation · `A=010120101 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00120` in some orientation · `A=010210202 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00120` in some orientation · `A=012120101 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C03 — word=UUDUUDDDD bites=- face=root apexes=[d2,d5,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `00120`:
|
||||
25 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010101212 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010202121 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `00120`:
|
||||
16 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00120` in some orientation · `A=012101202 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00120` in some orientation · `A=012102101 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00120` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
8 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00120` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `00120` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00120` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `00120`:
|
||||
12 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22012` → canonical `00120` · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:2 d5:0 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `11021` → canonical `00120` · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:1 d5:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22012`, realises `00120` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:2 d5:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00120` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `00120` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11021`, realises `00120` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:1 d5:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02221`, realises `00120` in some orientation · `A=012101012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `00120` in some orientation · `A=012102021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00120` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `00120` in some orientation · `A=012120201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00012`, realises `00120` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:0 d5:0 d6:1 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `00120`:
|
||||
23 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010101021 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010102021 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010201012 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010202012 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=012021012 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010101021 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010121201 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010121202 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010202012 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010212101 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010212102 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00120` in some orientation · `A=012101202 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `00120`:
|
||||
12 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `11201` → canonical `00120` · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u6:2] D[d2:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `00120` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u6:1] D[d2:1 d3:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `00120` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `00120` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `00120` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `00120` in some orientation · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `00120` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `00120`:
|
||||
11 colouring(s) with down-apex sequence `00120`:
|
||||
|
||||
- face apexes (raw labels) `22102` → canonical `00120` · `A=010102021 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `00120` in some orientation · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `00120` in some orientation · `A=010102021 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010120201 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `00120` in some orientation · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00120` in some orientation · `A=010201201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `00120` in some orientation · `A=010202101 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `00120` in some orientation · `A=010210201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `00120` in some orientation · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `00120` in some orientation · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `00120` in some orientation · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `01002`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
|
||||
- Realised by **7** of 10 configs (M(T), inner face).
|
||||
- **16** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **68** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_01002.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01002`:
|
||||
12 colouring(s) with down-apex sequence `01002`:
|
||||
|
||||
- face apexes (raw labels) `01002` → canonical `01002` · `A=010120121 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `02001` → canonical `01002` · `A=010210212 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `01002` → canonical `01002` · `A=012120121 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01002` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01002` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01002` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01002` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01002` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01002` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01002` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01002` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01002` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01002`:
|
||||
8 colouring(s) with down-apex sequence `01002`:
|
||||
|
||||
- face apexes (raw labels) `02001` → canonical `01002` · `A=012101212 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `01002` → canonical `01002` · `A=012102121 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `01002` → canonical `01002` · `A=012120121 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01002` in some orientation · `A=012101201 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01002` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01002` in some orientation · `A=012102102 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01002` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01002` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01002` in some orientation · `A=012120121 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01002` in some orientation · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `01002`:
|
||||
14 colouring(s) with down-apex sequence `01002`:
|
||||
|
||||
- face apexes (raw labels) `02001` → canonical `01002` · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `01002` → canonical `01002` · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01002` in some orientation · `A=010102012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01002` in some orientation · `A=010102102 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01002` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01002` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01002` in some orientation · `A=010201021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01002` in some orientation · `A=010201201 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01002` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01002` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01002` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01002` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01002` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01002` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01002` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `01002`:
|
||||
16 colouring(s) with down-apex sequence `01002`:
|
||||
|
||||
- face apexes (raw labels) `20221` → canonical `01002` · `A=010121012 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `10112` → canonical `01002` · `A=010212021 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `10112` → canonical `01002` · `A=012012021 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `02001` → canonical `01002` · `A=012101212 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:0 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `01002` → canonical `01002` · `A=012102121 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01002` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01002` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20221`, realises `01002` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20212`, realises `01002` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01002` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01002` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01002` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01002` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01002` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01002` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01002` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01002` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02212`, realises `01002` in some orientation · `A=012101021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01002` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01121`, realises `01002` in some orientation · `A=012102012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01002` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:0 d6:0 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01002`:
|
||||
4 colouring(s) with down-apex sequence `01002`:
|
||||
|
||||
- face apexes (raw labels) `02001` → canonical `01002` · `A=012101212 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01002` in some orientation · `A=012101201 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01002` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01002` in some orientation · `A=012121021 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01002`:
|
||||
6 colouring(s) with down-apex sequence `01002`:
|
||||
|
||||
- face apexes (raw labels) `02001` → canonical `01002` · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01002` in some orientation · `A=012010121 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01002` in some orientation · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01002` in some orientation · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01002` in some orientation · `A=012012101 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01002` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u6:2] D[d2:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01002`:
|
||||
8 colouring(s) with down-apex sequence `01002`:
|
||||
|
||||
- face apexes (raw labels) `02001` → canonical `01002` · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01002` in some orientation · `A=010201021 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01002` in some orientation · `A=010201202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01002` in some orientation · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01002` in some orientation · `A=010202102 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01002` in some orientation · `A=012010201 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01002` in some orientation · `A=012020102 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01002` in some orientation · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01002` in some orientation · `A=012121012 U[u0:2 u2:0 u4:0 u6:2] D[d1:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `01020`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
|
||||
- Realised by **4** of 10 configs (M(T), inner face).
|
||||
- **12** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 10 configs (M(T), inner face).
|
||||
- **68** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_01020.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
12 colouring(s) with down-apex sequence `01020`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01020` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01020` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01020` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01020` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01020` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01020` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01020` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01020` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01020` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
8 colouring(s) with down-apex sequence `01020`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01020` in some orientation · `A=012101201 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01020` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01020` in some orientation · `A=012102102 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01020` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01020` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01020` in some orientation · `A=012120121 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01020` in some orientation · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01020`:
|
||||
14 colouring(s) with down-apex sequence `01020`:
|
||||
|
||||
- face apexes (raw labels) `21202` → canonical `01020` · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `12101` → canonical `01020` · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `12101` → canonical `01020` · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01020` in some orientation · `A=010102012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01020` in some orientation · `A=010102102 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01020` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01020` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01020` in some orientation · `A=010201021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01020` in some orientation · `A=010201201 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01020` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01020` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01020` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01020` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01020` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01020` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01020` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `01020`:
|
||||
16 colouring(s) with down-apex sequence `01020`:
|
||||
|
||||
- face apexes (raw labels) `21202` → canonical `01020` · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:2 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `20212` → canonical `01020` · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `12101` → canonical `01020` · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `10121` → canonical `01020` · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `12101` → canonical `01020` · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `10121` → canonical `01020` · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01020` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01020` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20221`, realises `01020` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20212`, realises `01020` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01020` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01020` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01020` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01020` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01020` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01020` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01020` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01020` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02212`, realises `01020` in some orientation · `A=012101021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01020` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01121`, realises `01020` in some orientation · `A=012102012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01020` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:0 d6:0 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `01020`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01020` in some orientation · `A=012101201 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01020` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01020` in some orientation · `A=012121021 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `01020`:
|
||||
6 colouring(s) with down-apex sequence `01020`:
|
||||
|
||||
- face apexes (raw labels) `12101` → canonical `01020` · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `12101` → canonical `01020` · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01020` in some orientation · `A=012010121 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01020` in some orientation · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01020` in some orientation · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01020` in some orientation · `A=012012101 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01020` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u6:2] D[d2:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01020`:
|
||||
8 colouring(s) with down-apex sequence `01020`:
|
||||
|
||||
- face apexes (raw labels) `21202` → canonical `01020` · `A=010201021 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01020` in some orientation · `A=010201021 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01020` in some orientation · `A=010201202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01020` in some orientation · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01020` in some orientation · `A=010202102 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01020` in some orientation · `A=012010201 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01020` in some orientation · `A=012020102 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01020` in some orientation · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01020` in some orientation · `A=012121012 U[u0:2 u2:0 u4:0 u6:2] D[d1:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `01112`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 1×colour0, 3×colour1, 1×colour2.
|
||||
- Realised by **9** of 10 configs (M(T), inner face).
|
||||
- **33** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **10** of 10 configs (M(T), inner face).
|
||||
- **161** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_01112.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUUDDDDD bites=- face=root apexes=[d4,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `01112`:
|
||||
30 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010101212 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010102121 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010201212 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010202121 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=012101212 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=012102121 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010102101 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010201202 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=012102101 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C01 — word=UUUDUDDDD bites=- face=root apexes=[d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01112`:
|
||||
15 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010101212 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010202121 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=012101212 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
9 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01112` in some orientation · `A=010120101 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01112` in some orientation · `A=010210202 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01112` in some orientation · `A=012120101 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C03 — word=UUDUUDDDD bites=- face=root apexes=[d2,d5,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `01112`:
|
||||
25 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010101212 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010121212 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010202121 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010212121 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=012012121 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010101212 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010202121 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01112`:
|
||||
16 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01112` in some orientation · `A=012101202 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01112` in some orientation · `A=012102101 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01112` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01112`:
|
||||
8 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01112` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01112` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01112` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `01112`:
|
||||
12 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010121212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:0 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010212121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=012012121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `02221` → canonical `01112` · `A=012101012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:2 d8:1]`
|
||||
- face apexes (raw labels) `01112` → canonical `01112` · `A=012102021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `01112` → canonical `01112` · `A=012120201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22012`, realises `01112` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:2 d5:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01112` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01112` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11021`, realises `01112` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:1 d5:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02221`, realises `01112` in some orientation · `A=012101012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `01112` in some orientation · `A=012102021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01112` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `01112` in some orientation · `A=012120201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00012`, realises `01112` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:0 d5:0 d6:1 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `01112`:
|
||||
23 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010101021 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010121201 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010121202 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010202012 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010212101 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010212102 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01112` in some orientation · `A=012101202 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `01112`:
|
||||
12 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `10002` → canonical `01112` · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u6:2] D[d2:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01112` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u6:1] D[d2:1 d3:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01112` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01112` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01112` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01112` in some orientation · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01112` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01112`:
|
||||
11 colouring(s) with down-apex sequence `01112`:
|
||||
|
||||
- face apexes (raw labels) `20001` → canonical `01112` · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01112` in some orientation · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01112` in some orientation · `A=010102021 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010120201 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01112` in some orientation · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01112` in some orientation · `A=010201201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01112` in some orientation · `A=010202101 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01112` in some orientation · `A=010210201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01112` in some orientation · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01112` in some orientation · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01112` in some orientation · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `01121`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 1×colour0, 3×colour1, 1×colour2.
|
||||
- Realised by **4** of 10 configs (M(T), inner face).
|
||||
- **12** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 10 configs (M(T), inner face).
|
||||
- **68** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_01121.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
12 colouring(s) with down-apex sequence `01121`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01121` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01121` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01121` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01121` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01121` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01121` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01121` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01121` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01121` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
8 colouring(s) with down-apex sequence `01121`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01121` in some orientation · `A=012101201 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01121` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01121` in some orientation · `A=012102102 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01121` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01121` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01121` in some orientation · `A=012120121 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01121` in some orientation · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `01121`:
|
||||
14 colouring(s) with down-apex sequence `01121`:
|
||||
|
||||
- face apexes (raw labels) `21101` → canonical `01121` · `A=010102012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `21101` → canonical `01121` · `A=010120212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `12202` → canonical `01121` · `A=010201021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `12202` → canonical `01121` · `A=010210121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `12202` → canonical `01121` · `A=012010121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01121` in some orientation · `A=010102012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01121` in some orientation · `A=010102102 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01121` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01121` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01121` in some orientation · `A=010201021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01121` in some orientation · `A=010201201 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01121` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01121` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01121` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01121` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01121` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01121` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01121` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `01121`:
|
||||
16 colouring(s) with down-apex sequence `01121`:
|
||||
|
||||
- face apexes (raw labels) `21101` → canonical `01121` · `A=010120212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:1 d6:0 d8:1]`
|
||||
- face apexes (raw labels) `12202` → canonical `01121` · `A=010210121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `12202` → canonical `01121` · `A=012010121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apexes (raw labels) `02212` → canonical `01121` · `A=012101021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:1 d8:2]`
|
||||
- face apexes (raw labels) `01121` → canonical `01121` · `A=012102012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01121` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01121` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20221`, realises `01121` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20212`, realises `01121` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01121` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01121` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01121` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01121` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01121` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01121` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01121` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01121` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02212`, realises `01121` in some orientation · `A=012101021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01121` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01121`, realises `01121` in some orientation · `A=012102012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01121` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:0 d6:0 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `01121`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01121` in some orientation · `A=012101201 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01121` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01121` in some orientation · `A=012121021 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01121`:
|
||||
6 colouring(s) with down-apex sequence `01121`:
|
||||
|
||||
- face apexes (raw labels) `12202` → canonical `01121` · `A=012010121 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01121` in some orientation · `A=012010121 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01121` in some orientation · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01121` in some orientation · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01121` in some orientation · `A=012012101 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01121` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u6:2] D[d2:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01121`:
|
||||
8 colouring(s) with down-apex sequence `01121`:
|
||||
|
||||
- face apexes (raw labels) `21101` → canonical `01121` · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01121` in some orientation · `A=010201021 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01121` in some orientation · `A=010201202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01121` in some orientation · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01121` in some orientation · `A=010202102 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01121` in some orientation · `A=012010201 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01121` in some orientation · `A=012020102 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01121` in some orientation · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01121` in some orientation · `A=012121012 U[u0:2 u2:0 u4:0 u6:2] D[d1:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `01200`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
|
||||
- Realised by **9** of 10 configs (M(T), inner face).
|
||||
- **32** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **10** of 10 configs (M(T), inner face).
|
||||
- **161** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_01200.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUUDDDDD bites=- face=root apexes=[d4,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `01200`:
|
||||
30 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010102101 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010201202 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=012102101 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C01 — word=UUUDUDDDD bites=- face=root apexes=[d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01200`:
|
||||
15 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
9 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01200` in some orientation · `A=010120101 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01200` in some orientation · `A=010210202 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01200` in some orientation · `A=012120101 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C03 — word=UUDUUDDDD bites=- face=root apexes=[d2,d5,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `01200`:
|
||||
25 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010101201 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010121201 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010202102 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010212102 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=012012102 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010101212 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010202121 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01200`:
|
||||
16 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01200` in some orientation · `A=012101202 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01200` in some orientation · `A=012102101 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01200` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `01200`:
|
||||
8 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `21022` → canonical `01200` · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `12011` → canonical `01200` · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01200` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01200` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01200` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `01200`:
|
||||
12 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `21022` → canonical `01200` · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 d6:2 d8:2]`
|
||||
- face apexes (raw labels) `12011` → canonical `01200` · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22012`, realises `01200` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:2 d5:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01200` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01200` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11021`, realises `01200` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:1 d5:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02221`, realises `01200` in some orientation · `A=012101012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `01200` in some orientation · `A=012102021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01200` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `01200` in some orientation · `A=012120201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00012`, realises `01200` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:0 d5:0 d6:1 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `01200`:
|
||||
23 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010120201 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010121201 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010210102 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010212102 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010101021 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010121201 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010121202 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010202012 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010212101 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010212102 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01200` in some orientation · `A=012101202 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01200`:
|
||||
12 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10211` → canonical `01200` · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `12011` → canonical `01200` · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u6:2] D[d2:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01200` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u6:1] D[d2:1 d3:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01200` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01200` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01200` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01200` in some orientation · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01200` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `01200`:
|
||||
11 colouring(s) with down-apex sequence `01200`:
|
||||
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010120201 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `21022` → canonical `01200` · `A=010201201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `21022` → canonical `01200` · `A=010202101 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `20122` → canonical `01200` · `A=010210201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01200` in some orientation · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01200` in some orientation · `A=010102021 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010120201 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01200` in some orientation · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01200` in some orientation · `A=010201201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01200` in some orientation · `A=010202101 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01200` in some orientation · `A=010210201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01200` in some orientation · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01200` in some orientation · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01200` in some orientation · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:2 d8:2]`
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# Inner-face down-apex sequence `01211`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 1×colour0, 3×colour1, 1×colour2.
|
||||
- Realised by **6** of 10 configs (M(T), inner face).
|
||||
- **15** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 10 configs (M(T), inner face).
|
||||
- **68** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_01211.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
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|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01211`:
|
||||
12 colouring(s) with down-apex sequence `01211`:
|
||||
|
||||
- face apexes (raw labels) `01211` → canonical `01211` · `A=010120102 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `02122` → canonical `01211` · `A=010210201 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `01211` → canonical `01211` · `A=012120102 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01211` in some orientation · `A=010120102 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01211` in some orientation · `A=010120121 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=010121012 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01211` in some orientation · `A=010121021 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01211` in some orientation · `A=010210201 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01211` in some orientation · `A=010210212 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=010212012 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01211` in some orientation · `A=010212021 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01211` in some orientation · `A=012120102 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01211` in some orientation · `A=012120121 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=012121012 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01211` in some orientation · `A=012121021 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01211`:
|
||||
8 colouring(s) with down-apex sequence `01211`:
|
||||
|
||||
- face apexes (raw labels) `02122` → canonical `01211` · `A=012101201 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `01211` → canonical `01211` · `A=012102102 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `01211` → canonical `01211` · `A=012120102 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01211` in some orientation · `A=012101201 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01211` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01211` in some orientation · `A=012102102 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01211` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01211` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01211` in some orientation · `A=012120121 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01211` in some orientation · `A=012121021 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01211`:
|
||||
14 colouring(s) with down-apex sequence `01211`:
|
||||
|
||||
- face apexes (raw labels) `21011` → canonical `01211` · `A=010102102 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `12022` → canonical `01211` · `A=010201201 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `01211` → canonical `01211` · `A=012120102 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01211` in some orientation · `A=010102012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01211` in some orientation · `A=010102102 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01211` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01211` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01211` in some orientation · `A=010201021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01211` in some orientation · `A=010201201 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01211` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01211` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01211` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01211` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01211` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01211` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u6:0] D[d2:0 d4:1 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01211` in some orientation · `A=012120102 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=012121012 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
16 colouring(s) with down-apex sequence `01211`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01211` in some orientation · `A=010120121 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01211` in some orientation · `A=010120212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:1 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20221`, realises `01211` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20212`, realises `01211` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01211` in some orientation · `A=010210121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01211` in some orientation · `A=010210212 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01211` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01211` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01211` in some orientation · `A=012010121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:2 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01211` in some orientation · `A=012010212 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:2 d5:1 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10121`, realises `01211` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10112`, realises `01211` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02212`, realises `01211` in some orientation · `A=012101021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01211` in some orientation · `A=012101212 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01121`, realises `01211` in some orientation · `A=012102012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01002`, realises `01211` in some orientation · `A=012102121 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:0 d6:0 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01211`:
|
||||
4 colouring(s) with down-apex sequence `01211`:
|
||||
|
||||
- face apexes (raw labels) `02122` → canonical `01211` · `A=012101201 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01211` in some orientation · `A=012101201 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01211` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00102`, realises `01211` in some orientation · `A=012121021 U[u0:2 u1:0 u4:0 u5:2] D[d2:0 d3:0 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01211`:
|
||||
6 colouring(s) with down-apex sequence `01211`:
|
||||
|
||||
- face apexes (raw labels) `12022` → canonical `01211` · `A=012012101 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12202`, realises `01211` in some orientation · `A=012010121 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01211` in some orientation · `A=012010212 U[u0:2 u1:0 u4:2 u6:0] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12101`, realises `01211` in some orientation · `A=012012012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12022`, realises `01211` in some orientation · `A=012012101 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01211` in some orientation · `A=012101212 U[u0:2 u1:0 u4:2 u6:0] D[d2:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=012121012 U[u0:2 u1:0 u4:0 u6:2] D[d2:0 d3:0 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `01211`:
|
||||
8 colouring(s) with down-apex sequence `01211`:
|
||||
|
||||
- face apexes (raw labels) `21011` → canonical `01211` · `A=010201202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `21011` → canonical `01211` · `A=010202102 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `02122` → canonical `01211` · `A=012010201 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `01211` → canonical `01211` · `A=012020102 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21202`, realises `01211` in some orientation · `A=010201021 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01211` in some orientation · `A=010201202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21101`, realises `01211` in some orientation · `A=010202012 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21011`, realises `01211` in some orientation · `A=010202102 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02122`, realises `01211` in some orientation · `A=012010201 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01211`, realises `01211` in some orientation · `A=012020102 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02001`, realises `01211` in some orientation · `A=012101212 U[u0:2 u2:0 u4:2 u6:0] D[d1:0 d3:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `00201`, realises `01211` in some orientation · `A=012121012 U[u0:2 u2:0 u4:0 u6:2] D[d1:0 d3:0 d5:2 d7:0 d8:1]`
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# Inner-face down-apex sequence `01222`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 1×colour0, 1×colour1, 3×colour2.
|
||||
- Realised by **10** of 10 configs (M(T), inner face).
|
||||
- **36** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **161** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_01222.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUUDDDDD bites=- face=root apexes=[d4,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `01222`:
|
||||
30 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010101202 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010102101 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010201202 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010202101 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=012101202 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=012102101 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010102012 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010102021 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010102101 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010102102 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010102121 U[u0:2 u1:2 u2:2 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010201012 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010201021 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010201201 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010201202 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010201212 U[u0:2 u1:2 u2:1 u3:1] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u3:1] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u3:2] D[d4:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=012102012 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=012102021 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=012102101 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=012102102 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=012102121 U[u0:2 u1:0 u2:0 u3:2] D[d4:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C01 — word=UUUDUDDDD bites=- face=root apexes=[d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01222`:
|
||||
15 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010101202 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010202101 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=012101202 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010101201 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010101202 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010101212 U[u0:2 u1:2 u2:2 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010202101 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010202102 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010202121 U[u0:2 u1:2 u2:1 u4:1] D[d3:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=012101201 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=012101202 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=012101212 U[u0:2 u1:0 u2:0 u4:2] D[d3:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `01222`:
|
||||
9 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `01222` → canonical `01222` · `A=010120101 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `02111` → canonical `01222` · `A=010210202 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `01222` → canonical `01222` · `A=012120101 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010101021 U[u0:2 u1:2 u2:2 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01222` in some orientation · `A=010120101 U[u0:2 u1:2 u2:2 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010202012 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u2:1 u5:1] D[d3:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01222` in some orientation · `A=010210202 U[u0:2 u1:2 u2:1 u5:1] D[d3:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=012101012 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=012101021 U[u0:2 u1:0 u2:0 u5:2] D[d3:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01222` in some orientation · `A=012120101 U[u0:2 u1:0 u2:0 u5:2] D[d3:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C03 — word=UUDUUDDDD bites=- face=root apexes=[d2,d5,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `01222`:
|
||||
25 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010101202 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010121202 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010202101 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010212101 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=012012101 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010101202 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010101212 U[u0:2 u1:2 u3:2 u4:2] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010121012 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010121021 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u4:0] D[d2:2 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010202101 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010202121 U[u0:2 u1:2 u3:1 u4:1] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010212012 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010212021 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=012012012 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=012012021 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u4:0] D[d2:1 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `01222`:
|
||||
16 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010121202 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010212101 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=012012101 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `02111` → canonical `01222` · `A=012101202 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `01222` → canonical `01222` · `A=012102101 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `01222` → canonical `01222` · `A=012120101 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010101021 U[u0:2 u1:2 u3:2 u5:2] D[d2:2 d4:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010121201 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010121202 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u5:0] D[d2:2 d4:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010202012 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u5:1] D[d2:1 d4:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010212101 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010212102 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=012012101 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=012012102 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u5:0] D[d2:1 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01222` in some orientation · `A=012101202 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01222` in some orientation · `A=012102101 U[u0:2 u1:0 u3:2 u5:0] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01222` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u5:2] D[d2:0 d4:1 d6:2 d7:2 d8:2]`
|
||||
|
||||
## C05 — word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01222`:
|
||||
8 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `01222` → canonical `01222` · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01222` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u6:2] D[d2:2 d4:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u6:0] D[d2:2 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01222` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u3:1 u6:1] D[d2:1 d4:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u6:0] D[d2:1 d4:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01222` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u6:2] D[d2:0 d4:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
## C06 — word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `01222`:
|
||||
12 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `01222` → canonical `01222` · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22012`, realises `01222` in some orientation · `A=010101201 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:2 d5:0 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01222` in some orientation · `A=010102101 U[u0:2 u1:2 u3:2 u7:2] D[d2:2 d4:1 d5:0 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010121212 U[u0:2 u1:2 u3:0 u7:0] D[d2:2 d4:0 d5:0 d6:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01222` in some orientation · `A=010201202 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:2 d5:0 d6:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11021`, realises `01222` in some orientation · `A=010202102 U[u0:2 u1:2 u3:1 u7:1] D[d2:1 d4:1 d5:0 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010212121 U[u0:2 u1:2 u3:0 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=012012121 U[u0:2 u1:0 u3:2 u7:0] D[d2:1 d4:0 d5:0 d6:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02221`, realises `01222` in some orientation · `A=012101012 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:2 d5:2 d6:2 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `01222` in some orientation · `A=012102021 U[u0:2 u1:0 u3:2 u7:0] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01222` in some orientation · `A=012120101 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:2 d6:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `01112`, realises `01222` in some orientation · `A=012120201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:1 d5:1 d6:1 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `00012`, realises `01222` in some orientation · `A=012121201 U[u0:2 u1:0 u3:0 u7:2] D[d2:0 d4:0 d5:0 d6:1 d8:2]`
|
||||
|
||||
## C07 — word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8]
|
||||
|
||||
5 colouring(s) with down-apex sequence `01222`:
|
||||
23 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010120202 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010121202 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010210101 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010212101 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `02111` → canonical `01222` · `A=012101202 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010101021 U[u0:2 u1:2 u4:2 u5:2] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010102012 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010120212 U[u0:2 u1:2 u4:1 u5:1] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010121201 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010121202 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u5:0] D[d2:2 d3:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010201021 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010202012 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u5:1] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010210121 U[u0:2 u1:2 u4:2 u5:2] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010212101 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010212102 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u5:0] D[d2:1 d3:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=012021021 U[u0:2 u1:0 u4:0 u5:2] D[d2:1 d3:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01222` in some orientation · `A=012101202 U[u0:2 u1:0 u4:2 u5:0] D[d2:0 d3:2 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C08 — word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `01222`:
|
||||
12 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `10222` → canonical `01222` · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u1:2 u4:2 u6:2] D[d2:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010102021 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010120201 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010120202 U[u0:2 u1:2 u4:1 u6:1] D[d2:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010121212 U[u0:2 u1:2 u4:0 u6:0] D[d2:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=010201012 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11102`, realises `01222` in some orientation · `A=010202021 U[u0:2 u1:2 u4:1 u6:1] D[d2:1 d3:1 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10222`, realises `01222` in some orientation · `A=010210101 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `10211`, realises `01222` in some orientation · `A=010210102 U[u0:2 u1:2 u4:2 u6:2] D[d2:1 d3:0 d5:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `10002`, realises `01222` in some orientation · `A=010212121 U[u0:2 u1:2 u4:0 u6:0] D[d2:1 d3:0 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `12011`, realises `01222` in some orientation · `A=012012102 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:2 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `11201`, realises `01222` in some orientation · `A=012021012 U[u0:2 u1:0 u4:0 u6:2] D[d2:1 d3:1 d5:2 d7:0 d8:1]`
|
||||
|
||||
## C09 — word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `01222`:
|
||||
11 colouring(s) with down-apex sequence `01222`:
|
||||
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `20111` → canonical `01222` · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `02111` → canonical `01222` · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `01222` → canonical `01222` · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `22201`, realises `01222` in some orientation · `A=010101012 U[u0:2 u2:2 u4:2 u6:2] D[d1:2 d3:2 d5:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `22102`, realises `01222` in some orientation · `A=010102021 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:2 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010120201 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010120202 U[u0:2 u2:2 u4:1 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `20001`, realises `01222` in some orientation · `A=010121212 U[u0:2 u2:2 u4:0 u6:0] D[d1:2 d3:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01222` in some orientation · `A=010201201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `21022`, realises `01222` in some orientation · `A=010202101 U[u0:2 u2:1 u4:1 u6:2] D[d1:2 d3:1 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20122`, realises `01222` in some orientation · `A=010210201 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `20111`, realises `01222` in some orientation · `A=010210202 U[u0:2 u2:1 u4:2 u6:1] D[d1:2 d3:0 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `02111`, realises `01222` in some orientation · `A=012010202 U[u0:2 u2:1 u4:2 u6:1] D[d1:0 d3:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `01222`, realises `01222` in some orientation · `A=012020101 U[u0:2 u2:1 u4:1 u6:2] D[d1:0 d3:1 d5:2 d7:2 d8:2]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face singleton-down-apex sequences of Kempe-balanced colourings (n=9, m=5)
|
||||
|
||||
Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedral class) that has an inner non-tooth face holding exactly 5 singleton down-tooth apexes: **10 configs (M(T), inner face)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the down-apex colour sequence in increasing annular-edge order, and reduce it modulo colour permutation (NOT dihedral symmetry).
|
||||
Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedral class) that has an inner non-tooth face holding exactly 5 singleton down-tooth apexes: **10 configs (M(T), inner face)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the down-apex colour sequence in cyclic order off the un-deduped census (every cyclic orientation of each colouring), and reduce it modulo colour permutation (NOT dihedral symmetry). Reading off the census makes the recorded vocabulary orientation-honest; see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Total Kempe-balanced colourings (mod colour permutation): **229**.
|
||||
- Distinct canonical down-apex sequences overall: **10**.
|
||||
@@ -9,31 +9,27 @@ Every full medial tire graph M(T) with |A(T)| = 9 (one representative per dihedr
|
||||
|
||||
| sequence | colour multiset | #configs realising | #colourings |
|
||||
|---|---|---|---|
|
||||
| `00012` | 3+1+1 | 10 | 30 |
|
||||
| `00102` | 3+1+1 | 6 | 13 |
|
||||
| `00120` | 3+1+1 | 9 | 30 |
|
||||
| `01002` | 3+1+1 | 7 | 16 |
|
||||
| `01020` | 3+1+1 | 4 | 12 |
|
||||
| `01112` | 3+1+1 | 9 | 33 |
|
||||
| `01121` | 3+1+1 | 4 | 12 |
|
||||
| `01200` | 3+1+1 | 9 | 32 |
|
||||
| `01211` | 3+1+1 | 6 | 15 |
|
||||
| `01222` | 3+1+1 | 10 | 36 |
|
||||
| `00012` | 3+1+1 | 10 | 161 |
|
||||
| `00102` | 3+1+1 | 7 | 68 |
|
||||
| `00120` | 3+1+1 | 10 | 161 |
|
||||
| `01002` | 3+1+1 | 7 | 68 |
|
||||
| `01020` | 3+1+1 | 7 | 68 |
|
||||
| `01112` | 3+1+1 | 10 | 161 |
|
||||
| `01121` | 3+1+1 | 7 | 68 |
|
||||
| `01200` | 3+1+1 | 10 | 161 |
|
||||
| `01211` | 3+1+1 | 7 | 68 |
|
||||
| `01222` | 3+1+1 | 10 | 161 |
|
||||
|
||||
Note: every realised sequence has its three colour-counts of **equal parity** — exactly the Kempe-parity constraint on the inner face (each colour pair meets its singleton down apexes an even number of times). With m = 5 apexes (m is odd) every count must be **odd**, so the only admissible colour multisets are 3+1+1.
|
||||
|
||||
## Step 4 — grouping configs by their set of unique down-apex sequences
|
||||
|
||||
The 10 configs fall into **6** groups by the set of canonical down-apex sequences they realise:
|
||||
The 10 configs fall into **2** groups by the set of canonical down-apex sequences they realise:
|
||||
|
||||
| #configs | set of down-apex sequences | config ids |
|
||||
|---|---|---|
|
||||
| 7 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } | C02, C04, C05, C06, C07, C08, C09 |
|
||||
| 3 | { `00012`, `00120`, `01112`, `01200`, `01222` } | C00, C01, C03 |
|
||||
| 2 | { `00012`, `00102`, `00120`, `01002`, `01112`, `01200`, `01211`, `01222` } | C04, C07 |
|
||||
| 2 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } | C08, C09 |
|
||||
| 1 | { `00012`, `00102`, `00120`, `01002`, `01211`, `01222` } | C02 |
|
||||
| 1 | { `00012`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01222` } | C06 |
|
||||
| 1 | { `00012`, `00102`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } | C05 |
|
||||
|
||||
## Config atlas (ids)
|
||||
|
||||
@@ -41,12 +37,12 @@ The 10 configs fall into **6** groups by the set of canonical down-apex sequence
|
||||
|---|---|---|---|
|
||||
| C00 | word=UUUUDDDDD bites=- face=root apexes=[d4,d5,d6,d7,d8] | 30 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
|
||||
| C01 | word=UUUDUDDDD bites=- face=root apexes=[d3,d5,d6,d7,d8] | 15 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
|
||||
| C02 | word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8] | 21 | { `00012`, `00102`, `00120`, `01002`, `01211`, `01222` } |
|
||||
| C02 | word=UUUDDUDDD bites=- face=root apexes=[d3,d4,d6,d7,d8] | 21 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
| C03 | word=UUDUUDDDD bites=- face=root apexes=[d2,d5,d6,d7,d8] | 25 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
|
||||
| C04 | word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8] | 24 | { `00012`, `00102`, `00120`, `01002`, `01112`, `01200`, `01211`, `01222` } |
|
||||
| C05 | word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8] | 22 | { `00012`, `00102`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
| C06 | word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8] | 28 | { `00012`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01222` } |
|
||||
| C07 | word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8] | 27 | { `00012`, `00102`, `00120`, `01002`, `01112`, `01200`, `01211`, `01222` } |
|
||||
| C04 | word=UUDUDUDDD bites=- face=root apexes=[d2,d4,d6,d7,d8] | 24 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
| C05 | word=UUDUDDUDD bites=- face=root apexes=[d2,d4,d5,d7,d8] | 22 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
| C06 | word=UUDUDDDUD bites=- face=root apexes=[d2,d4,d5,d6,d8] | 28 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
| C07 | word=UUDDUUDDD bites=- face=root apexes=[d2,d3,d6,d7,d8] | 27 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
| C08 | word=UUDDUDUDD bites=- face=root apexes=[d2,d3,d5,d7,d8] | 18 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
| C09 | word=UDUDUDUDD bites=- face=root apexes=[d1,d3,d5,d7,d8] | 19 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
|
||||
|
||||
|
||||
+7
-7
@@ -1,10 +1,10 @@
|
||||
# Inner-face down-apex sequence `000000`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 6×colour0.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **5** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **5** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_000000.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
@@ -13,24 +13,24 @@ Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D
|
||||
|
||||
2 colouring(s) with down-apex sequence `000000`:
|
||||
|
||||
- face apexes (raw labels) `222222` → canonical `000000` · `A=012010101 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `111111` → canonical `000000` · `A=012020202 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222222`, realises `000000` in some orientation · `A=012010101 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111111`, realises `000000` in some orientation · `A=012020202 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C01 — word=UUDUDDDDD bites=- face=root apexes=[d2,d4,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000000`:
|
||||
|
||||
- face apexes (raw labels) `111111` → canonical `000000` · `A=012020202 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111111`, realises `000000` in some orientation · `A=012020202 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000000`:
|
||||
|
||||
- face apexes (raw labels) `111111` → canonical `000000` · `A=012020202 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111111`, realises `000000` in some orientation · `A=012020202 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000000`:
|
||||
|
||||
- face apexes (raw labels) `111111` → canonical `000000` · `A=012020202 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111111`, realises `000000` in some orientation · `A=012020202 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `000011`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **5** of 7 configs (M(T), inner face).
|
||||
- **7** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 7 configs (M(T), inner face).
|
||||
- **42** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_000011.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUDDDDDD bites=- face=root apexes=[d3,d4,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `000011`:
|
||||
12 colouring(s) with down-apex sequence `000011`:
|
||||
|
||||
- face apexes (raw labels) `222211` → canonical `000011` · `A=012010102 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `111122` → canonical `000011` · `A=012020201 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `222211`, realises `000011` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222002`, realises `000011` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `000011` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `000011` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `000011` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `000011` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `000011` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `000011` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000011` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000011` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `000011` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `000011` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C01 — word=UUDUDDDDD bites=- face=root apexes=[d2,d4,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000011`:
|
||||
6 colouring(s) with down-apex sequence `000011`:
|
||||
|
||||
- face apexes (raw labels) `111122` → canonical `000011` · `A=012020201 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `000011` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `000011` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000011` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000011` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `000011` in some orientation · `A=012021202 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `000011` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000011`:
|
||||
6 colouring(s) with down-apex sequence `000011`:
|
||||
|
||||
- face apexes (raw labels) `111122` → canonical `000011` · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `000011` in some orientation · `A=012020101 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `000011` in some orientation · `A=012020102 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000011` in some orientation · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000011` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `000011` in some orientation · `A=012120101 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000011` in some orientation · `A=012120202 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000011`:
|
||||
4 colouring(s) with down-apex sequence `000011`:
|
||||
|
||||
- face apexes (raw labels) `111122` → canonical `000011` · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `122111`, realises `000011` in some orientation · `A=012010202 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000011` in some orientation · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000011` in some orientation · `A=012020212 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000011` in some orientation · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `000011`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `000011` in some orientation · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `000011` in some orientation · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `000011` in some orientation · `A=012120101 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000011` in some orientation · `A=012120202 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `000011`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `211222`, realises `000011` in some orientation · `A=010202101 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `000011` in some orientation · `A=010212101 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `000011` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000011` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `000011`:
|
||||
6 colouring(s) with down-apex sequence `000011`:
|
||||
|
||||
- face apexes (raw labels) `000022` → canonical `000011` · `A=012121201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `000011` → canonical `000011` · `A=012121202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `000011` in some orientation · `A=010120201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `000011` in some orientation · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `220022`, realises `000011` in some orientation · `A=010121201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000011` in some orientation · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000022`, realises `000011` in some orientation · `A=012121201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `000011`, realises `000011` in some orientation · `A=012121202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `000101`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **1** of 7 configs (M(T), inner face).
|
||||
- **1** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **20** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_000101.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `000101`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `000101` in some orientation · `A=012102101 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `000101` in some orientation · `A=012102121 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `000101`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `000101` in some orientation · `A=012012101 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `000101` in some orientation · `A=012012121 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `000101` in some orientation · `A=012021202 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `000101` in some orientation · `A=012021212 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `000101` in some orientation · `A=012102101 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `000101` in some orientation · `A=012102121 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `000101`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `000101` in some orientation · `A=010201201 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `000101` in some orientation · `A=010201202 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `000101` in some orientation · `A=012012101 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `000101` in some orientation · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `000101` in some orientation · `A=012021202 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `000101` in some orientation · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000101`:
|
||||
6 colouring(s) with down-apex sequence `000101`:
|
||||
|
||||
- face apexes (raw labels) `000202` → canonical `000101` · `A=012121021 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `220202`, realises `000101` in some orientation · `A=010121021 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `000101` in some orientation · `A=010210201 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `000101` in some orientation · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `011101`, realises `000101` in some orientation · `A=012020212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `000101` in some orientation · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000202`, realises `000101` in some orientation · `A=012121021 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `000110`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **5** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 7 configs (M(T), inner face).
|
||||
- **42** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_000110.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUDDDDDD bites=- face=root apexes=[d3,d4,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `000110`:
|
||||
12 colouring(s) with down-apex sequence `000110`:
|
||||
|
||||
- face apexes (raw labels) `222002` → canonical `000110` · `A=012010121 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `111001` → canonical `000110` · `A=012020212 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222211`, realises `000110` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222002`, realises `000110` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `000110` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `000110` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `000110` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `000110` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `000110` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `000110` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000110` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000110` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `000110` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `000110` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C01 — word=UUDUDDDDD bites=- face=root apexes=[d2,d4,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000110`:
|
||||
6 colouring(s) with down-apex sequence `000110`:
|
||||
|
||||
- face apexes (raw labels) `111001` → canonical `000110` · `A=012020212 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `000110` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `000110` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000110` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000110` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `000110` in some orientation · `A=012021202 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `000110` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000110`:
|
||||
6 colouring(s) with down-apex sequence `000110`:
|
||||
|
||||
- face apexes (raw labels) `111001` → canonical `000110` · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `000110` in some orientation · `A=012020101 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `000110` in some orientation · `A=012020102 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000110` in some orientation · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000110` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `000110` in some orientation · `A=012120101 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000110` in some orientation · `A=012120202 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `000110`:
|
||||
4 colouring(s) with down-apex sequence `000110`:
|
||||
|
||||
- face apexes (raw labels) `111001` → canonical `000110` · `A=012020212 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `122111`, realises `000110` in some orientation · `A=012010202 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `000110` in some orientation · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `000110` in some orientation · `A=012020212 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000110` in some orientation · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `000110`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `000110` in some orientation · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `000110` in some orientation · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `000110` in some orientation · `A=012120101 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000110` in some orientation · `A=012120202 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `000110`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `211222`, realises `000110` in some orientation · `A=010202101 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `000110` in some orientation · `A=010212101 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `000110` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000110` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `000110`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `000110` in some orientation · `A=010120201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `000110` in some orientation · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `220022`, realises `000110` in some orientation · `A=010121201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `000110` in some orientation · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000022`, realises `000110` in some orientation · `A=012121201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `000011`, realises `000110` in some orientation · `A=012121202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
|
||||
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@@ -1,10 +1,10 @@
|
||||
# Inner-face down-apex sequence `001001`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **6** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **8** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_001001.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
@@ -13,25 +13,27 @@ Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D
|
||||
|
||||
2 colouring(s) with down-apex sequence `001001`:
|
||||
|
||||
- face apexes (raw labels) `002002` → canonical `001001` · `A=012120121 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `001001` → canonical `001001` · `A=012120212 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `002002`, realises `001001` in some orientation · `A=012120121 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `001001` in some orientation · `A=012120212 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001001`:
|
||||
2 colouring(s) with down-apex sequence `001001`:
|
||||
|
||||
- face apexes (raw labels) `001001` → canonical `001001` · `A=012120212 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `122122`, realises `001001` in some orientation · `A=012010201 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `001001` in some orientation · `A=012120212 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001001`:
|
||||
|
||||
- face apexes (raw labels) `002002` → canonical `001001` · `A=012120121 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `001001` → canonical `001001` · `A=012120212 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `002002`, realises `001001` in some orientation · `A=012120121 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `001001` in some orientation · `A=012120212 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001001`:
|
||||
2 colouring(s) with down-apex sequence `001001`:
|
||||
|
||||
- face apexes (raw labels) `001001` → canonical `001001` · `A=012120212 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `211211`, realises `001001` in some orientation · `A=010202102 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `001001` in some orientation · `A=012120212 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
|
||||
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+39
-5
@@ -1,17 +1,51 @@
|
||||
# Inner-face down-apex sequence `001010`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **1** of 7 configs (M(T), inner face).
|
||||
- **1** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **20** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_001010.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001010`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `001010` in some orientation · `A=012102101 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `001010` in some orientation · `A=012102121 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `001010`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `001010` in some orientation · `A=012012101 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `001010` in some orientation · `A=012012121 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `001010` in some orientation · `A=012021202 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `001010` in some orientation · `A=012021212 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `001010` in some orientation · `A=012102101 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `001010` in some orientation · `A=012102121 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `001010`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `001010` in some orientation · `A=010201201 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `001010` in some orientation · `A=010201202 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `001010` in some orientation · `A=012012101 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `001010` in some orientation · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `001010` in some orientation · `A=012021202 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `001010` in some orientation · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001010`:
|
||||
6 colouring(s) with down-apex sequence `001010`:
|
||||
|
||||
- face apexes (raw labels) `220202` → canonical `001010` · `A=010121021 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `220202`, realises `001010` in some orientation · `A=010121021 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `001010` in some orientation · `A=010210201 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `001010` in some orientation · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `011101`, realises `001010` in some orientation · `A=012020212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `001010` in some orientation · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000202`, realises `001010` in some orientation · `A=012121021 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
|
||||
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# Inner-face down-apex sequence `001100`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **6** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 7 configs (M(T), inner face).
|
||||
- **42** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_001100.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUDDDDDD bites=- face=root apexes=[d3,d4,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001100`:
|
||||
12 colouring(s) with down-apex sequence `001100`:
|
||||
|
||||
- face apexes (raw labels) `221122` → canonical `001100` · `A=012010201 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `112211` → canonical `001100` · `A=012020102 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222211`, realises `001100` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222002`, realises `001100` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `001100` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `001100` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `001100` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `001100` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `001100` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `001100` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001100` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001100` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `001100` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `001100` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C01 — word=UUDUDDDDD bites=- face=root apexes=[d2,d4,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001100`:
|
||||
6 colouring(s) with down-apex sequence `001100`:
|
||||
|
||||
- face apexes (raw labels) `112211` → canonical `001100` · `A=012020102 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `001100` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `001100` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001100` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001100` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `001100` in some orientation · `A=012021202 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `001100` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001100`:
|
||||
6 colouring(s) with down-apex sequence `001100`:
|
||||
|
||||
- face apexes (raw labels) `112211` → canonical `001100` · `A=012020102 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `001100` in some orientation · `A=012020101 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `001100` in some orientation · `A=012020102 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001100` in some orientation · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001100` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `001100` in some orientation · `A=012120101 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001100` in some orientation · `A=012120202 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `001100`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `122111`, realises `001100` in some orientation · `A=012010202 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001100` in some orientation · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001100` in some orientation · `A=012020212 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001100` in some orientation · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `001100`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `001100` in some orientation · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `001100` in some orientation · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `001100` in some orientation · `A=012120101 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001100` in some orientation · `A=012120202 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `001100`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `211222`, realises `001100` in some orientation · `A=010202101 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `001100` in some orientation · `A=010212101 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `001100` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001100` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001100`:
|
||||
6 colouring(s) with down-apex sequence `001100`:
|
||||
|
||||
- face apexes (raw labels) `221122` → canonical `001100` · `A=010120201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `220022` → canonical `001100` · `A=010121201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `001100` in some orientation · `A=010120201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `001100` in some orientation · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `220022`, realises `001100` in some orientation · `A=010121201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001100` in some orientation · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000022`, realises `001100` in some orientation · `A=012121201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `000011`, realises `001100` in some orientation · `A=012121202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `001111`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 4×colour1.
|
||||
- Realised by **7** of 7 configs (M(T), inner face).
|
||||
- **12** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **42** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_001111.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUDDDDDD bites=- face=root apexes=[d3,d4,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001111`:
|
||||
12 colouring(s) with down-apex sequence `001111`:
|
||||
|
||||
- face apexes (raw labels) `221111` → canonical `001111` · `A=012010202 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `112222` → canonical `001111` · `A=012020101 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `222211`, realises `001111` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222002`, realises `001111` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `001111` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `001111` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `001111` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `001111` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `001111` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `001111` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001111` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001111` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `001111` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `001111` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C01 — word=UUDUDDDDD bites=- face=root apexes=[d2,d4,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001111`:
|
||||
6 colouring(s) with down-apex sequence `001111`:
|
||||
|
||||
- face apexes (raw labels) `112222` → canonical `001111` · `A=012020101 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `001111` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `001111` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001111` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001111` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `001111` in some orientation · `A=012021202 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `001111` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `001111`:
|
||||
6 colouring(s) with down-apex sequence `001111`:
|
||||
|
||||
- face apexes (raw labels) `112222` → canonical `001111` · `A=012020101 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `002222` → canonical `001111` · `A=012120101 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `001111` → canonical `001111` · `A=012120202 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `001111` in some orientation · `A=012020101 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `001111` in some orientation · `A=012020102 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001111` in some orientation · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001111` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `001111` in some orientation · `A=012120101 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001111` in some orientation · `A=012120202 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001111`:
|
||||
4 colouring(s) with down-apex sequence `001111`:
|
||||
|
||||
- face apexes (raw labels) `001111` → canonical `001111` · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `122111`, realises `001111` in some orientation · `A=012010202 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `001111` in some orientation · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `001111` in some orientation · `A=012020212 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001111` in some orientation · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001111`:
|
||||
4 colouring(s) with down-apex sequence `001111`:
|
||||
|
||||
- face apexes (raw labels) `002222` → canonical `001111` · `A=012120101 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `001111` → canonical `001111` · `A=012120202 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `001111` in some orientation · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `001111` in some orientation · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `001111` in some orientation · `A=012120101 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001111` in some orientation · `A=012120202 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001111`:
|
||||
4 colouring(s) with down-apex sequence `001111`:
|
||||
|
||||
- face apexes (raw labels) `001111` → canonical `001111` · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `211222`, realises `001111` in some orientation · `A=010202101 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `001111` in some orientation · `A=010212101 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `001111` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001111` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001111`:
|
||||
6 colouring(s) with down-apex sequence `001111`:
|
||||
|
||||
- face apexes (raw labels) `221111` → canonical `001111` · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `001111` → canonical `001111` · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `001111` in some orientation · `A=010120201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `001111` in some orientation · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `220022`, realises `001111` in some orientation · `A=010121201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `001111` in some orientation · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000022`, realises `001111` in some orientation · `A=012121201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `000011`, realises `001111` in some orientation · `A=012121202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
|
||||
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@@ -1,10 +1,10 @@
|
||||
# Inner-face down-apex sequence `001122`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
|
||||
- Realised by **5** of 7 configs (M(T), inner face).
|
||||
- **8** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **11** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_001122.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
@@ -13,32 +13,35 @@ Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D
|
||||
|
||||
2 colouring(s) with down-apex sequence `001122`:
|
||||
|
||||
- face apexes (raw labels) `002211` → canonical `001122` · `A=012120102 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `001122` → canonical `001122` · `A=012120201 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `002211`, realises `001122` in some orientation · `A=012120102 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001122`, realises `001122` in some orientation · `A=012120201 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:2 d8:2]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001122`:
|
||||
2 colouring(s) with down-apex sequence `001122`:
|
||||
|
||||
- face apexes (raw labels) `001122` → canonical `001122` · `A=012120201 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `122001`, realises `001122` in some orientation · `A=012010212 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001122`, realises `001122` in some orientation · `A=012120201 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:2 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001122`:
|
||||
|
||||
- face apexes (raw labels) `002211` → canonical `001122` · `A=012120102 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `001122` → canonical `001122` · `A=012120201 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `002211`, realises `001122` in some orientation · `A=012120102 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001122`, realises `001122` in some orientation · `A=012120201 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:2 d8:2]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001122`:
|
||||
2 colouring(s) with down-apex sequence `001122`:
|
||||
|
||||
- face apexes (raw labels) `001122` → canonical `001122` · `A=012120201 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `211002`, realises `001122` in some orientation · `A=010202121 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001122`, realises `001122` in some orientation · `A=012120201 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:2 d8:2]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001122`:
|
||||
3 colouring(s) with down-apex sequence `001122`:
|
||||
|
||||
- face apexes (raw labels) `220011` → canonical `001122` · `A=010121202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `001122` → canonical `001122` · `A=012120201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `220011`, realises `001122` in some orientation · `A=010121202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `211002`, realises `001122` in some orientation · `A=010202121 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:1 d5:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001122`, realises `001122` in some orientation · `A=012120201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:2 d8:2]`
|
||||
|
||||
|
||||
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+53
@@ -0,0 +1,53 @@
|
||||
# Inner-face down-apex sequence `001212`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
|
||||
- Realised by **5** of 7 configs (M(T), inner face).
|
||||
- **17** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_001212.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `001212` in some orientation · `A=012102021 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `001212` in some orientation · `A=012102102 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `120201`, realises `001212` in some orientation · `A=012012012 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `001212` in some orientation · `A=012102021 U[u0:2 u1:0 u5:1] D[d2:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `001212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `001212` in some orientation · `A=012012021 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `001212` in some orientation · `A=012012102 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012201`, realises `001212` in some orientation · `A=012021012 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010122`, realises `001212` in some orientation · `A=012021201 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `001212` in some orientation · `A=012102021 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `001212` in some orientation · `A=012102102 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `001212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `212001`, realises `001212` in some orientation · `A=010201212 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `001212` in some orientation · `A=012012102 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010122`, realises `001212` in some orientation · `A=012021201 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `001212` in some orientation · `A=012102021 U[u0:2 u2:0 u5:1] D[d1:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `001212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `212001`, realises `001212` in some orientation · `A=010201212 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210102`, realises `001212` in some orientation · `A=010212021 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:0 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `011202`, realises `001212` in some orientation · `A=012020121 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:2 d7:0 d8:2]`
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `001221`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
|
||||
- Realised by **3** of 7 configs (M(T), inner face).
|
||||
- **4** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **5** of 7 configs (M(T), inner face).
|
||||
- **13** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_001221.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUDDDDDD bites=- face=root apexes=[d3,d4,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001221`:
|
||||
6 colouring(s) with down-apex sequence `001221`:
|
||||
|
||||
- face apexes (raw labels) `221001` → canonical `001221` · `A=012010212 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `112002` → canonical `001221` · `A=012020121 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221001`, realises `001221` in some orientation · `A=012010212 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `201102`, realises `001221` in some orientation · `A=012012021 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200211`, realises `001221` in some orientation · `A=012012102 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `112002`, realises `001221` in some orientation · `A=012020121 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102201`, realises `001221` in some orientation · `A=012021012 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100122`, realises `001221` in some orientation · `A=012021201 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:1 d7:2 d8:2]`
|
||||
|
||||
## C01 — word=UUDUDDDDD bites=- face=root apexes=[d2,d4,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001221`:
|
||||
3 colouring(s) with down-apex sequence `001221`:
|
||||
|
||||
- face apexes (raw labels) `112002` → canonical `001221` · `A=012020121 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112002`, realises `001221` in some orientation · `A=012020121 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `102201`, realises `001221` in some orientation · `A=012021012 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100122`, realises `001221` in some orientation · `A=012021201 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:1 d7:2 d8:2]`
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001221`:
|
||||
|
||||
- face apexes (raw labels) `112002` → canonical `001221` · `A=012020121 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112002`, realises `001221` in some orientation · `A=012020121 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `001221`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `201102`, realises `001221` in some orientation · `A=010212021 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200211`, realises `001221` in some orientation · `A=010212102 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `001221`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `200211`, realises `001221` in some orientation · `A=010212102 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
|
||||
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+26
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@@ -1,38 +1,51 @@
|
||||
# Inner-face down-apex sequence `010001`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **7** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **20** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_010001.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010001`:
|
||||
2 colouring(s) with down-apex sequence `010001`:
|
||||
|
||||
- face apexes (raw labels) `020002` → canonical `010001` · `A=012102121 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010001` in some orientation · `A=012102101 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010001` in some orientation · `A=012102121 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `010001`:
|
||||
6 colouring(s) with down-apex sequence `010001`:
|
||||
|
||||
- face apexes (raw labels) `020002` → canonical `010001` · `A=012012121 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `010001` → canonical `010001` · `A=012021212 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apexes (raw labels) `020002` → canonical `010001` · `A=012102121 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010001` in some orientation · `A=012012101 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010001` in some orientation · `A=012012121 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `010001` in some orientation · `A=012021202 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010001` in some orientation · `A=012021212 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010001` in some orientation · `A=012102101 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010001` in some orientation · `A=012102121 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010001`:
|
||||
6 colouring(s) with down-apex sequence `010001`:
|
||||
|
||||
- face apexes (raw labels) `020002` → canonical `010001` · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apexes (raw labels) `010001` → canonical `010001` · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `010001` in some orientation · `A=010201201 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `010001` in some orientation · `A=010201202 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010001` in some orientation · `A=012012101 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010001` in some orientation · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `010001` in some orientation · `A=012021202 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010001` in some orientation · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010001`:
|
||||
6 colouring(s) with down-apex sequence `010001`:
|
||||
|
||||
- face apexes (raw labels) `010001` → canonical `010001` · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `220202`, realises `010001` in some orientation · `A=010121021 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `010001` in some orientation · `A=010210201 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `010001` in some orientation · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `011101`, realises `010001` in some orientation · `A=012020212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010001` in some orientation · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000202`, realises `010001` in some orientation · `A=012121021 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
|
||||
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@@ -0,0 +1,39 @@
|
||||
# Inner-face down-apex sequence `010010`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **8** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_010010.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010010`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `002002`, realises `010010` in some orientation · `A=012120121 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `010010` in some orientation · `A=012120212 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010010`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `122122`, realises `010010` in some orientation · `A=012010201 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `010010` in some orientation · `A=012120212 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010010`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `002002`, realises `010010` in some orientation · `A=012120121 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `010010` in some orientation · `A=012120212 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010010`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `211211`, realises `010010` in some orientation · `A=010202102 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001001`, realises `010010` in some orientation · `A=012120212 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `010100`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **2** of 7 configs (M(T), inner face).
|
||||
- **2** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **20** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_010100.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010100`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010100` in some orientation · `A=012102101 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010100` in some orientation · `A=012102121 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `010100`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010100` in some orientation · `A=012012101 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010100` in some orientation · `A=012012121 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `010100` in some orientation · `A=012021202 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010100` in some orientation · `A=012021212 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010100` in some orientation · `A=012102101 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010100` in some orientation · `A=012102121 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010100`:
|
||||
6 colouring(s) with down-apex sequence `010100`:
|
||||
|
||||
- face apexes (raw labels) `212122` → canonical `010100` · `A=010201201 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `010100` in some orientation · `A=010201201 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `010100` in some orientation · `A=010201202 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010100` in some orientation · `A=012012101 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010100` in some orientation · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `010100` in some orientation · `A=012021202 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010100` in some orientation · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010100`:
|
||||
6 colouring(s) with down-apex sequence `010100`:
|
||||
|
||||
- face apexes (raw labels) `212122` → canonical `010100` · `A=010210201 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `220202`, realises `010100` in some orientation · `A=010121021 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `010100` in some orientation · `A=010210201 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `010100` in some orientation · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `011101`, realises `010100` in some orientation · `A=012020212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010100` in some orientation · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000202`, realises `010100` in some orientation · `A=012121021 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `010111`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 4×colour1.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **8** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- **20** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_010111.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010111`:
|
||||
2 colouring(s) with down-apex sequence `010111`:
|
||||
|
||||
- face apexes (raw labels) `020222` → canonical `010111` · `A=012102101 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010111` in some orientation · `A=012102101 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010111` in some orientation · `A=012102121 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `010111`:
|
||||
6 colouring(s) with down-apex sequence `010111`:
|
||||
|
||||
- face apexes (raw labels) `020222` → canonical `010111` · `A=012012101 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `010111` → canonical `010111` · `A=012021202 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `020222` → canonical `010111` · `A=012102101 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010111` in some orientation · `A=012012101 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010111` in some orientation · `A=012012121 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `010111` in some orientation · `A=012021202 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010111` in some orientation · `A=012021212 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010111` in some orientation · `A=012102101 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010111` in some orientation · `A=012102121 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `010111`:
|
||||
6 colouring(s) with down-apex sequence `010111`:
|
||||
|
||||
- face apexes (raw labels) `212111` → canonical `010111` · `A=010201202 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `020222` → canonical `010111` · `A=012012101 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `010111` → canonical `010111` · `A=012021202 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `010111` in some orientation · `A=010201201 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `010111` in some orientation · `A=010201202 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020222`, realises `010111` in some orientation · `A=012012101 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020002`, realises `010111` in some orientation · `A=012012121 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `010111`, realises `010111` in some orientation · `A=012021202 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010111` in some orientation · `A=012021212 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010111`:
|
||||
6 colouring(s) with down-apex sequence `010111`:
|
||||
|
||||
- face apexes (raw labels) `212111` → canonical `010111` · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `220202`, realises `010111` in some orientation · `A=010121021 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:2 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212122`, realises `010111` in some orientation · `A=010210201 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `212111`, realises `010111` in some orientation · `A=010210202 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:2 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `011101`, realises `010111` in some orientation · `A=012020212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:1 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010001`, realises `010111` in some orientation · `A=012021212 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:0 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000202`, realises `010111` in some orientation · `A=012121021 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:2 d7:0 d8:2]`
|
||||
|
||||
|
||||
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-16
@@ -1,32 +1,53 @@
|
||||
# Inner-face down-apex sequence `010122`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
|
||||
- Realised by **3** of 7 configs (M(T), inner face).
|
||||
- **6** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **5** of 7 configs (M(T), inner face).
|
||||
- **17** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_010122.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010122`:
|
||||
2 colouring(s) with down-apex sequence `010122`:
|
||||
|
||||
- face apexes (raw labels) `020211` → canonical `010122` · `A=012102102 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010122` in some orientation · `A=012102021 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010122` in some orientation · `A=012102102 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `010122`:
|
||||
|
||||
- face apexes (raw labels) `020211` → canonical `010122` · `A=012012102 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `010122` → canonical `010122` · `A=012021201 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `020211` → canonical `010122` · `A=012102102 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010122`:
|
||||
|
||||
- face apexes (raw labels) `020211` → canonical `010122` · `A=012012102 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apexes (raw labels) `010122` → canonical `010122` · `A=012021201 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `120201`, realises `010122` in some orientation · `A=012012012 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010122` in some orientation · `A=012102021 U[u0:2 u1:0 u5:1] D[d2:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `010122`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010122` in some orientation · `A=012012021 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010122` in some orientation · `A=012012102 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012201`, realises `010122` in some orientation · `A=012021012 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010122`, realises `010122` in some orientation · `A=012021201 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010122` in some orientation · `A=012102021 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010122` in some orientation · `A=012102102 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
4 colouring(s) with down-apex sequence `010122`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `212001`, realises `010122` in some orientation · `A=010201212 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010122` in some orientation · `A=012012102 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010122`, realises `010122` in some orientation · `A=012021201 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010122` in some orientation · `A=012102021 U[u0:2 u2:0 u5:1] D[d1:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `010122`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `212001`, realises `010122` in some orientation · `A=010201212 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210102`, realises `010122` in some orientation · `A=010212021 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:0 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `011202`, realises `010122` in some orientation · `A=012020121 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:2 d7:0 d8:2]`
|
||||
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `010212`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
|
||||
- Realised by **4** of 7 configs (M(T), inner face).
|
||||
- **7** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_010212.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021201`, realises `010212` in some orientation · `A=012102012 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:1 d6:2 d7:0 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `120102`, realises `010212` in some orientation · `A=012012021 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:0 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021201`, realises `010212` in some orientation · `A=012102012 U[u0:2 u1:0 u5:1] D[d2:0 d3:2 d4:1 d6:2 d7:0 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
3 colouring(s) with down-apex sequence `010212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021201`, realises `010212` in some orientation · `A=012012012 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:1 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012102`, realises `010212` in some orientation · `A=012021021 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:2 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021201`, realises `010212` in some orientation · `A=012102012 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:1 d6:2 d7:0 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010212`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021201`, realises `010212` in some orientation · `A=012102012 U[u0:2 u2:0 u5:1] D[d1:0 d3:2 d4:1 d6:2 d7:0 d8:1]`
|
||||
|
||||
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|
||||
# Inner-face down-apex sequence `010221`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
|
||||
- Realised by **2** of 7 configs (M(T), inner face).
|
||||
- **2** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **5** of 7 configs (M(T), inner face).
|
||||
- **17** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_010221.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010221`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010221` in some orientation · `A=012102021 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010221` in some orientation · `A=012102102 U[u0:2 u1:0 u4:1] D[d2:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `010221`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `120201`, realises `010221` in some orientation · `A=012012012 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:0 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010221` in some orientation · `A=012102021 U[u0:2 u1:0 u5:1] D[d2:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `010221`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010221` in some orientation · `A=012012021 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010221` in some orientation · `A=012012102 U[u0:2 u2:1 u4:0] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `012201`, realises `010221` in some orientation · `A=012021012 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:2 d6:2 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010122`, realises `010221` in some orientation · `A=012021201 U[u0:2 u2:1 u4:0] D[d1:0 d3:1 d5:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010221` in some orientation · `A=012102021 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010221` in some orientation · `A=012102102 U[u0:2 u2:0 u4:1] D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010221`:
|
||||
4 colouring(s) with down-apex sequence `010221`:
|
||||
|
||||
- face apexes (raw labels) `212001` → canonical `010221` · `A=010201212 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `212001`, realises `010221` in some orientation · `A=010201212 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:2 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `020211`, realises `010221` in some orientation · `A=012012102 U[u0:2 u2:1 u5:0] D[d1:0 d3:2 d4:0 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `010122`, realises `010221` in some orientation · `A=012021201 U[u0:2 u2:1 u5:0] D[d1:0 d3:1 d4:0 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `021102`, realises `010221` in some orientation · `A=012102021 U[u0:2 u2:0 u5:1] D[d1:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `010221`:
|
||||
3 colouring(s) with down-apex sequence `010221`:
|
||||
|
||||
- face apexes (raw labels) `212001` → canonical `010221` · `A=010201212 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `212001`, realises `010221` in some orientation · `A=010201212 U[u0:2 u3:1 u6:0] D[d1:2 d2:1 d4:2 d5:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `210102`, realises `010221` in some orientation · `A=010212021 U[u0:2 u3:0 u6:1] D[d1:2 d2:1 d4:0 d5:1 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `011202`, realises `010221` in some orientation · `A=012020121 U[u0:2 u3:1 u6:0] D[d1:0 d2:1 d4:1 d5:2 d7:0 d8:2]`
|
||||
|
||||
|
||||
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@@ -1,43 +1,88 @@
|
||||
# Inner-face down-apex sequence `011000`
|
||||
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in increasing annular-edge order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**.
|
||||
Canonical colour sequence of the singleton down-tooth apexes on a single inner non-tooth face (read in cyclic order, reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 singleton down apexes on the face**. Sequences are read off the un-deduped census (every cyclic orientation of each colouring), so one colouring may realise several sequences -- see `../kempe_sequence_orientation_note.md`.
|
||||
|
||||
- Colour multiset: 4×colour0, 2×colour1.
|
||||
- Realised by **5** of 7 configs (M(T), inner face).
|
||||
- **7** Kempe-balanced colourings (mod colour permutation) produce it.
|
||||
- Realised by **7** of 7 configs (M(T), inner face).
|
||||
- **42** Kempe-balanced colourings (mod colour permutation) realise it in some orientation.
|
||||
- Figure: `seq_011000.png` (black rings mark the face's down apexes).
|
||||
|
||||
Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours 0/1/2 = 0:orange, 1:blue, 2:green.
|
||||
|
||||
## C00 — word=UUUDDDDDD bites=- face=root apexes=[d3,d4,d5,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `011000`:
|
||||
12 colouring(s) with down-apex sequence `011000`:
|
||||
|
||||
- face apexes (raw labels) `200222` → canonical `011000` · `A=012012101 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `100111` → canonical `011000` · `A=012021202 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222211`, realises `011000` in some orientation · `A=012010102 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `222002`, realises `011000` in some orientation · `A=012010121 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:2 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `011000` in some orientation · `A=012010201 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `011000` in some orientation · `A=012010202 U[u0:2 u1:0 u2:1] D[d3:2 d4:2 d5:1 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `011000` in some orientation · `A=012012101 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `011000` in some orientation · `A=012012121 U[u0:2 u1:0 u2:1] D[d3:2 d4:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `011000` in some orientation · `A=012020101 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `011000` in some orientation · `A=012020102 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `011000` in some orientation · `A=012020201 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `011000` in some orientation · `A=012020212 U[u0:2 u1:0 u2:1] D[d3:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `011000` in some orientation · `A=012021202 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `011000` in some orientation · `A=012021212 U[u0:2 u1:0 u2:1] D[d3:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C01 — word=UUDUDDDDD bites=- face=root apexes=[d2,d4,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `011000`:
|
||||
6 colouring(s) with down-apex sequence `011000`:
|
||||
|
||||
- face apexes (raw labels) `100111` → canonical `011000` · `A=012021202 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `011000` in some orientation · `A=012020101 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `011000` in some orientation · `A=012020102 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `011000` in some orientation · `A=012020201 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `011000` in some orientation · `A=012020212 U[u0:2 u1:0 u3:1] D[d2:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100111`, realises `011000` in some orientation · `A=012021202 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `100001`, realises `011000` in some orientation · `A=012021212 U[u0:2 u1:0 u3:1] D[d2:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
|
||||
|
||||
## C02 — word=UUDDUDDDD bites=- face=root apexes=[d2,d3,d5,d6,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `011000`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `112222`, realises `011000` in some orientation · `A=012020101 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `112211`, realises `011000` in some orientation · `A=012020102 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:2 d6:2 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `011000` in some orientation · `A=012020201 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `011000` in some orientation · `A=012020212 U[u0:2 u1:0 u4:1] D[d2:1 d3:1 d5:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `011000` in some orientation · `A=012120101 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `011000` in some orientation · `A=012120202 U[u0:2 u1:0 u4:1] D[d2:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C03 — word=UUDDDUDDD bites=- face=root apexes=[d2,d3,d4,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `011000`:
|
||||
4 colouring(s) with down-apex sequence `011000`:
|
||||
|
||||
- face apexes (raw labels) `122111` → canonical `011000` · `A=012010202 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `122111`, realises `011000` in some orientation · `A=012010202 U[u0:2 u1:0 u5:1] D[d2:1 d3:2 d4:2 d6:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `111122`, realises `011000` in some orientation · `A=012020201 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `111001`, realises `011000` in some orientation · `A=012020212 U[u0:2 u1:0 u5:1] D[d2:1 d3:1 d4:1 d6:0 d7:0 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `011000` in some orientation · `A=012120202 U[u0:2 u1:0 u5:1] D[d2:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C04 — word=UDUDUDDDD bites=- face=root apexes=[d1,d3,d5,d6,d7,d8]
|
||||
|
||||
1 colouring(s) with down-apex sequence `011000`:
|
||||
4 colouring(s) with down-apex sequence `011000`:
|
||||
|
||||
- face apexes (raw labels) `200222` → canonical `011000` · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `011000` in some orientation · `A=010212101 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `011000` in some orientation · `A=010212121 U[u0:2 u2:1 u4:0] D[d1:2 d3:0 d5:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `002222`, realises `011000` in some orientation · `A=012120101 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `011000` in some orientation · `A=012120202 U[u0:2 u2:0 u4:1] D[d1:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C05 — word=UDUDDUDDD bites=- face=root apexes=[d1,d3,d4,d6,d7,d8]
|
||||
|
||||
2 colouring(s) with down-apex sequence `011000`:
|
||||
4 colouring(s) with down-apex sequence `011000`:
|
||||
|
||||
- face apexes (raw labels) `211222` → canonical `011000` · `A=010202101 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apexes (raw labels) `200222` → canonical `011000` · `A=010212101 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `211222`, realises `011000` in some orientation · `A=010202101 U[u0:2 u2:1 u5:0] D[d1:2 d3:1 d4:1 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200222`, realises `011000` in some orientation · `A=010212101 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:2 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `200002`, realises `011000` in some orientation · `A=010212121 U[u0:2 u2:1 u5:0] D[d1:2 d3:0 d4:0 d6:0 d7:0 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `011000` in some orientation · `A=012120202 U[u0:2 u2:0 u5:1] D[d1:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
|
||||
|
||||
## C06 — word=UDDUDDUDD bites=- face=root apexes=[d1,d2,d4,d5,d7,d8]
|
||||
|
||||
6 colouring(s) with down-apex sequence `011000`:
|
||||
|
||||
- face apex colours (canonical-rep edge order) `221122`, realises `011000` in some orientation · `A=010120201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `221111`, realises `011000` in some orientation · `A=010120202 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `220022`, realises `011000` in some orientation · `A=010121201 U[u0:2 u3:0 u6:1] D[d1:2 d2:2 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `001111`, realises `011000` in some orientation · `A=012120202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:1 d5:1 d7:1 d8:1]`
|
||||
- face apex colours (canonical-rep edge order) `000022`, realises `011000` in some orientation · `A=012121201 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:2 d8:2]`
|
||||
- face apex colours (canonical-rep edge order) `000011`, realises `011000` in some orientation · `A=012121202 U[u0:2 u3:0 u6:1] D[d1:0 d2:0 d4:0 d5:0 d7:1 d8:1]`
|
||||
|
||||
|
||||
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Reference in New Issue
Block a user