Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site qubix.UUCP Path: utzoo!linus!decvax!decwrl!sun!qubix!lab From: lab@qubix.UUCP (Q-Bick) Newsgroups: net.math Subject: Re: Archemedian polyhedra: the EPCOT ball Message-ID: <1395@qubix.UUCP> Date: Tue, 2-Oct-84 00:44:25 EDT Article-I.D.: qubix.1395 Posted: Tue Oct 2 00:44:25 1984 Date-Received: Wed, 3-Oct-84 05:44:52 EDT References: <3732@decwrl.UUCP> Organization: Qubix Graphic Systems, Saratoga, CA Lines: 36 I guess I qualify as an engineer. During my first visit to EPCOT (8 Oct 1982), I studied the ball in an attempt to determine its basic geometric construction. I don't know if I still have the notes, so I'll pass along what I can remember. Side point to return to later: each triangle of the geodesic dome is covered by a triangular pyramid, thus multiplying the total number of triangles on the dome by 3. Back to the basic dome. The ground perspective made it difficult to correlate with the most obvious similar structure - an icosahedron. As you enter EPCOT, you can immediate see a couple of super-triangles, 8 units per side, on the front. Further, there is a trough extend from the top of one to the top of the dome. At that vertex and at the ends of common edge of the first two triangles, you can see the intersection of FIVE basic triangles. But waitaminnit - if the dome was based on an icosahedron, I should not have been able to see as much as I did above and below those first two triangles (even accounting for curvature). Hmmm...new theory is called for. It became apparent that there had to be places where SIX curved triangular faces met. With planar faces, this would be obvious; the curved faces could conceal this well. I came up with a 30-face construction; with 8 units per side, this put 1080 on the basic dome and 3240 on the entire ball, minus a few for the base. Will check my EPCOT photos (I have some from both sides of the dome) and report back later. However, I am also notoriously absent-minded - if you don't hear anything in a week or two, nag me about it. (BTW, although disk cameras are rotten for capturing facial detail, they did VERY well with the ridges and troughs on the dome!) -- The Ice Floe of Larry Bickford {amd,decwrl,sun,idi,ittvax}!qubix!lab You can't settle the issue until you've settled how to settle the issue.