diff --git a/colored_pentagon_reduction/example.py b/colored_pentagon_reduction/example.py
index 25f3e94..2b23cdd 100644
--- a/colored_pentagon_reduction/example.py
+++ b/colored_pentagon_reduction/example.py
@@ -155,6 +155,15 @@ def tutte_embedding(g: Graph, outer: list[Any]) -> dict[Any, tuple[float, float]
 
     return pos
 
+def get_embedding_from_pos(g: Graph) -> dict[Any, list[Any]]:
+    """Compute a combinatorial planar embedding by sorting each vertex's neighbors by angle."""
+    import math
+    pos = g.get_pos()
+    return {
+        v: sorted(g.neighbors(v), key=lambda w: math.atan2(pos[w][1] - pos[v][1], pos[w][0] - pos[v][0]))
+        for v in g.vertices()
+    }
+
 def _neighbors_form_cycle(g: Graph, v: Any) -> bool:
     """Return True if the neighbors of v induce a cycle in g."""
     return bool(cast(Graph, g.subgraph(g.neighbors(v))).is_cycle())
@@ -174,7 +183,7 @@ def pluck(g: Graph, coloring: VertexColoring, v0: Any) -> tuple[Graph, VertexCol
     g_prime.delete_vertex(v0)
     if (pos := g.get_pos()) is not None:
         g_prime.set_pos({v: p for v, p in pos.items() if v != v0})
-    g_prime.is_planar(set_embedding=True)
+        g_prime.set_embedding(get_embedding_from_pos(g_prime))
     coloring_prime = coloring.copy()
     del coloring_prime[v0]
     return g_prime, coloring_prime
@@ -211,7 +220,7 @@ def squish(g: Graph, coloring: VertexColoring, v0: Any) -> tuple[Graph, VertexCo
     g_prime.merge_vertices([v0, v1, v2])
     if (pos := g.get_pos()) is not None:
         g_prime.set_pos({v: p for v, p in pos.items() if v not in (v1, v2)})
-    g_prime.is_planar(set_embedding=True)
+        g_prime.set_embedding(get_embedding_from_pos(g_prime))
     coloring_prime = {v: c for v, c in coloring.items() if v not in (v1, v2)}
     coloring_prime[v0] = coloring[v1]
     return g_prime, coloring_prime, v1, v2