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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: 10,232
Registered: 7/15/05
Re: convex polyhedra with all faces regular
Posted: Dec 9, 2012 1:51 PM
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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



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