[r-t] Methods as polyhedra
Mark Davies
mark at snowtiger.net
Wed Apr 9 22:32:33 UTC 2008
Pabs asks,
> Aren't the graphs of these isomorphic to the icosohedron or dodecahedron?
No - some are isomorphic to simpler convex polyhedra, e.g. the nonconvex
tetrahemihexahedron is edge and vertex equivalent to the regular
octahedron - and some appear not to be isomorphic to any uniform convex
polyhedron at all: for example Wikipedia tells me that the "great
dirhombicosidodecahedron" is edge and vertex equivalent to the "compound of
twenty tetrahemihexahedra" which is a uniform polyhedral compound, not a
uniform polyhedron.
<http://en.wikipedia.org/wiki/Great_dirhombicosidodecahedron>
And then there is the "great disnub dirhombidodecahedron", which apparently
is even weirder... but still has a useful 60 vertices.
MBD
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