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.

