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From: td@alice.UUCP (Tom Duff)
Newsgroups: net.math
Subject: Re: Archemedian polyhedra
Message-ID: <3008@alice.UUCP>
Date: Thu, 27-Sep-84 03:27:25 EDT
Article-I.D.: alice.3008
Posted: Thu Sep 27 03:27:25 1984
Date-Received: Fri, 28-Sep-84 04:13:52 EDT
References: <3732@decwrl.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
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The best work I know about polyhedra with regular faces is
	Adventures among the Toroids
	published by the author
	B.M. Stuart
	4494 Wausau Road
	Okemos, Michigan 48864
This is an amazing book.  It consists of about 200 hand-lettered pages,
illustrated by the author and published privately.  I was introduced to this
volume by Lee Dickey (watmath!ljdickey), a frequent contributor to this group.
There is material in Stewart's book of interest to geometers
working at all levels from rank amateur to University professional.  It may
be hard to find.  My copy is 11 years old, and starting to show its age.
Nominally, the book is about enumerating a particular class of regular-faced
polyhedra pierced by one or more holes, but its scope is quite broad.  It is
a treasure-house of beautiful mathematics and beautiful illustrations.  Nowhere
else can you find a proof of the Frobenius-Burnside counting formula on one
page, and an illustrated discussion of women's underwear on the next (pp 195-6.)

More easily acquired is H.S.M. Coxeter's Regular Polytopes, 2nd ed., Macmillan,
N.Y., 1963.  There may be a more recent edition of this one.  Coxeter is
probably the 20th century's greatest geometer.

I actually learned this stuff from a volume called Mathematical Models,
which I believe is by Cundy & Rollett, 2nd ed., Oxford, 1960.  In high school
this book (or another of the same title, I only have a second-hand reference
to it now) was one of my favorite books.  The book is full of descriptions of
things you can build that illustrate various mathematical notions.