moroney@jon.DEC (09/25/84)
To: alice!td Sorry, I misunderstood you. I just associated a Greek name applied to polyhedra to the 5 Platonic solids. Ignore my last message (although the part about the edge duals holds) However, I would guess that ~80% of those reading your last message made the same mistake. You should have explained what Archemedians were (I never heard of them until now) to prevent confusion. Can you point me to reference material on this subject? I am fascinated by this subject. Also, how many sides/edges/vertices each has? Too bad you can't send models over the net, I would ask for them, too. To those who would like to know what certain common shapes are, a soccer ball (with faces flattened) is a 'truncated icosahedron' and the 3-dimensional stop sign which started this discussion is a 'rhombicuboctahedron' (correct me if I am wrong) (sorry, lost the name of the original poster) Stupid Question of the Day: Is the huge ball of the Epcot Center in Disney World a fair die? (ignore the base, holes, etc. of course) How many sides does it have? (same assumptions as above) Mike Moroney ..decvax!decwrl!rhea!jon!moroney
td@alice.UUCP (Tom Duff) (09/27/84)
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.
brucec@orca.UUCP (10/01/84)
--------------------------- [This is a snap Turing Test; it represents 10% of your final grade] >> 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. There is a more recent edition; the third, published by Dover Publications, Inc., 180 Varick St., New York, NY 10014, copyright 1973. If you can't find it in a local bookstore, you can order direct from Dover. If you are interested in seeing what models of the solids look like, see "Spherical Models" by Magnus J. Wenninger, Cambridge University Press, 1979. There is another book called "Dual Models" which I believe is also published by the Cambridge Press. I have seen it, but I don't own a copy, so I can't give you the author's name or the publication date. Bruce Cohen UUCP: ...!tektronix!orca!brucec CSNET: orca!brucec@tektronix ARPA: orca!brucec.tektronix@rand-relay USMail: M/S 61-183 Tektronix, Inc. P.O. Box 1000 Wilsonville, OR 97070