Date: Dec 9, 2012 1:51 PM
Subject: Re: convex polyhedra with all faces regular
Phil Carmody wrote:
>> Prove or disprove:
>> For each positive integer n, there are only finitely many
>> convex polyhedra, up to similarity, such that all faces are
>> regular polygons (not necessarily of the same type) with at
>> most n edges.
>Are we to assume Euclidean geometry? I suspect with a closed
>geometry, the answer would be very different.
Yes, Euclidean geometry.
The polyhedra are assumed to be in R^3.
>Then again, you'd want to exclude degenerate polyhedra even
>in the Euclidean case.
Yes, assume the polyhedra are convex and non-degenerate
(positive volume) with no two faces coplanar.