Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site alice.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!alice!td 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 Lines: 27 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.