didericis
8cc94fb6b9
Name A(T) the "annular cycle" (Thm 3.3, Def 3.4); clarify the bite-face condition in Remark 3.8 to count down-tooth apexes interior to each face; add the non-incidence stipulation for bite edges to Def 3.7. Add an exhaustive generator over |A(T)| enforcing the 3.1-3.9 properties (tooth word, non-crossing non-incident bites, >=3 up teeth, bite-face condition), plus a plotting script and the n=9 atlas (81 dihedral classes). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
47 lines
3.9 KiB
TeX
47 lines
3.9 KiB
TeX
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A full medial tire graph $\mathsf {M}(T)$ illustrating the tooth terminology. The thick cycle is the annular medial cycle $A(T)$, whose black vertices are the annular medial vertices. Each edge of $A(T)$ carries one tooth: up teeth (blue apexes, outer-boundary medial vertices) point into the outer region, and down teeth (red apexes, inner-boundary medial vertices) point into the inner region. The two down teeth meeting at the central shared apex (larger red vertex) form a bite; that shared apex splits the inner region into two faces, one with four down teeth on its boundary and one with none.}}{4}{}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Three six-face full medial tire graphs found by the boundary-state restriction search. Black vertices are annular medial vertices; blue vertices are outer boundary medial vertices and red vertices are inner boundary medial vertices. The word below each diagram records the outer/inner type of the six annular faces in cyclic order. Boundary states are identified only up to colour permutation, not by rotation or reflection of the boundary order.}}{5}{}\protected@file@percent }
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