I'm trying to prove that there are an unbounded number of (non-isomorphic) 3-regular planar graphs with faces of degree 3 or 6. I know that there are only 4 faces of degree 3 in such a graph. I cannot find a way to recursively generate such graphs, however. I have looked at some examples but was unable to find any recurring pattern.
2026-03-30 06:48:56.1774853336
Recursively generate 3-regular planar graphs
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One recursive construction is to take a picture like the following, with a triangle surrounded by "layers" of hexagons:
Then, put four of these pictures together as the sides of a tetrahedron.