User talk:Tomruen/Polyhedra by vertex figures

This list could be useful in a search for uniform tilings of H3. —Tamfang 01:01, 18 April 2006 (UTC)[reply]

I'm not sure exactly what you mean. Uniform tilings of H2? Infinite polyhedra of E3? This list so far excludes vertex figures with positive angle defect that don't exist in known polyhedra. I was most interested in using it for convex "near-miss" Johnson solids. Tom Ruen 04:17, 18 April 2006 (UTC)[reply]

Considering only the vertex figures of uniform solids, one could fairly easily enumerate the irregular polyhedra that can be formed from such figures and inscribed in a sphere. Some of these would be the vertex figures of tilings of E3, of S3 (i.e. polychora), or of H3 (hyperbolic 3-space). —Tamfang 04:36, 18 April 2006 (UTC)[reply]