Definition of uniform polytope

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Definition of uniform polytope

Postby quickfur » Fri Nov 07, 2008 1:24 am

The current HDDB definition of a uniform polytope is a vertex-transitive polytope. This is not the definition used by the Uniform Polychora Project... their definition specifies that all surtopes must be uniform polytopes as well. Without this condition, we will also get polytopes with non-uniform facets, such as the dual of the bitruncated 24-cell, and the dual of the mesotruncates of all simplices in 4D and higher (these are all Catalans). These are convex; there may be many other non-convex, non-uniform vertex-transitive polytopes as well. And there may be others besides these.
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Re: Definition of uniform polytope

Postby Keiji » Fri Nov 07, 2008 5:58 am

I updated the page.

Stuff like this belongs on the talk pages on HDDB, though, not here...
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