@OscarCunningham@mathstodon.xyz
2026-08-01 06:10 UTC
Replies (4)
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@ianh@mastodon.social 2026-08-01 07:30
@OscarCunningham@mathstodon.xyz i wrote a program that enumerates all the colorings, and it doesn't find any that work: http://ianhenderson.org/2026-08-01-dodecahedron.c.txt (the face numberings were from putting labels on a real-life icosahedron i had handy, so i could have made mistakes during that process, but the group it generates does have order 60 at least)
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@vnikolov@ieji.de 2026-08-01 07:57
For each face, I suppose. (I guess not.) It might be an interesting problem to find the maximum number of faces for which this can be achieved, since it's trivially possible for a single face (if I am not mistaken working it out in my head). @OscarCunningham@mathstodon.xyz
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@jmopp@masto.ai 2026-08-01 08:26
@OscarCunningham@mathstodon.xyz First thought is that it's equivalent to finding a colouring of the dodecahedral graph such that every 6-tuple of a node and its neighbours has a unique colouring up to rotation. There are at most 4096 2-colourings of a graph with 12 nodes, so it's very brute-forceable. And I see someone beat me to it.
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@ngons@mathstodon.xyz 2026-08-01 09:15
@OscarCunningham@mathstodon.xyz but if it doesn’t work, what is the minimum amount of colours?