Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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


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

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

Advanced Search
Reply to this Topic Reply to this Topic

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 1994-2013. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.