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Topic: convex polyhedron with almost all faces regular
Replies: 6   Last Post: Dec 6, 2012 5:43 PM

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 dy/dx Posts: 6 Registered: 11/10/12
Re: convex polyhedron with almost all faces regular
Posted: Dec 6, 2012 10:33 AM

On Tue, 4 Dec 2012 16:17:22 -0800 (PST), 1treePetrifiedForestLane wrote:

> yes; the consequence of "one irregular facet" are to weird.
>

>> "then all of the faces are regular polygons" as being true ...

It's clear that if all but one of the polygons is *equilateral*, then they
all must be.

However, I exhibit a counterexample to the claim that if all but one are
*regular* they all must be, if a dihedral angle of exactly 180 degrees is
permitted:

A rhombus with internal angles of 60 and 120 degrees, four square faces,
and two equilateral triangular faces, forming a prism. The two triangular
faces, combined, form a duplicate of the rhombic face.

Date Subject Author
12/4/12 quasi
12/4/12 David Bernier
12/4/12 Brian Q. Hutchings
12/5/12 Brian Q. Hutchings
12/6/12 dy/dx
12/6/12 quasi
12/6/12 Brian Q. Hutchings