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Topic: convex polyhedra with all faces regular
Replies: 7   Last Post: Dec 23, 2012 6:20 AM

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 quasi Posts: 11,740 Registered: 7/15/05
Re: convex polyhedra with all faces regular
Posted: Dec 9, 2012 1:51 PM

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

Date Subject Author
12/5/12 quasi
12/5/12 Brian Q. Hutchings
12/6/12 quasi
12/6/12 Brian Q. Hutchings
12/9/12 Phil Carmody
12/9/12 quasi
12/23/12 achille
12/23/12 quasi