Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
dy/dx

Posts: 6
Registered: 11/10/12
Re: convex polyhedron with almost all faces regular
Posted: Dec 6, 2012 10:33 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.