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From: dbc@cs.brown.edu (Brook Conner)
Newsgroups: comp.graphics
Subject: Re: Need references on drawing 3d regular polygonal solids
Summary: Jim Blinn's corner, and topology
Message-ID: <49433@brunix.UUCP>
Date: 9 Sep 90 15:11:03 GMT
References: <1990Sep9.095906.26612@rice.edu>
Sender: news@brunix.UUCP
Reply-To: dbc@cs.brown.edu (Brook Conner)
Organization: Brown University Department of Computer Science
Lines: 22

Dwayne,

The Platonic solid are the only regular solids because they are :)
Seriously, I'm sure this is a result of some result in topology  somewhere
(although having only a passing acquaintance with topology stemming from
working under a topologist (John Hughes of Foley, van Dam, Feiner, and Hughes)
I have yet to see this proof for myself, so I can't offer pointers to it)

But the real point of this post is how to draw them, which is discussed in
detail in "Jim Blinn's Corner" in IEEE Computer Graphics and Applications,
November 1987, volume 7 number 11, page 62.  Blinn presents sets of coords that
form a tetra hedron, octahedron, dodecahedron, and icosahedron (the cube is
left as an exercise for the reader :) using only 1.0, 0.0 and 1.618034 (i.e.  
(1 + sqrt(5))/2 ) and their additive inverses.

Brook


Brook Conner		| Klacktoveedsedstene
Brown Computer Graphics	| Fortune sez: Brook's Law -- Adding manpower to a late
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