Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10 5/3/83; site umcp-cs.UUCP
Path: utzoo!watmath!clyde!burl!mgnetp!ihnp4!zehntel!dual!amd!decwrl!decvax!mcnc!philabs!cmcl2!seismo!rlgvax!cvl!umcp-cs!randy
From: randy@umcp-cs.UUCP
Newsgroups: net.math
Subject: Semi-regular polyhedra
Message-ID: <7721@umcp-cs.UUCP>
Date: Mon, 2-Jul-84 14:49:35 EDT
Article-I.D.: umcp-cs.7721
Posted: Mon Jul  2 14:49:35 1984
Date-Received: Sun, 15-Jul-84 07:17:40 EDT
Distribution: net
Organization: Univ. of Maryland, Computer Science Dept.
Lines: 26

The recent mail on geometric duality brings to mind a question I've
had for some time.  Maybe someone out there can help me.  I'm wondering
what the list of all semi-regular polyhedra is.  (Recall that a semi-
regular polyhedron has all faces regular but not necessarily congruent,
but every vertex is congruent.  Thus the cuboctahedron is composed of
triangles and squares with exactly two triangles and two squares meeting
at every vertex.)

I tried to make a list and found that there seem to be *lots* more than
I expected.  For example, there is an infinite set of "cylinders" built
as follows:  For base and top choose a regular K sided polygon.  Then
for the walls of the cylinder use K squares.  At every vertex, you'll
have one K-gon and 2 squares meeting.  (You can also get a similar infinite
set using triangles as wall constructors providing K > 3.  Then you need 2*K
triangles.)

Anyway, I've found all sorts of unexpected (and rather pleasing) polygons 
with the help of a lisp program to generate legal possibilities.  I can
send details if anyone is interested.  But this *must* have been done
somewhere before.  Anybody got pointers?  Thanks.

		- Randy
-- 
Randy Trigg
...!seismo!umcp-cs!randy (Usenet)
randy%umcp-cs@CSNet-Relay (Arpanet)