Date: Dec 9, 2012 1:51 PM
Author: quasi
Subject: Re: convex polyhedra with all faces regular
Phil Carmody wrote:

>quasi writes:

>>

>> 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.

quasi