Path: utzoo!utgpu!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!mailrus!cornell!uw-beaver!rice!titan!foo
From: foo@titan.rice.edu (Mark Hall)
Newsgroups: comp.graphics
Subject: Re: Polygon Representation of a Sphere's Surface
Summary: you may have do discover a new "Platonic" solid
Message-ID: <2908@kalliope.rice.edu>
Date: 22 Mar 89 23:26:26 GMT
References: <270@ai.etl.army.mil>
Sender: usenet@rice.edu
Reply-To: foo@titan.rice.edu (Mark Hall)
Organization: Rice University, Houston
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In article <270@ai.etl.army.mil> richr@ai.etl.army.mil. (Richard Rosenthal) writes:
>I want to have in 3-D space (x, y, z) a polygon near-representation
>of the surface of a sphere where each polygon is identical
>and regular (if that's the word).
>
>Is an icosahedron the right place to start?
>
>I would like to be able to generate the representation with
>increasing numbers of polygons, say first 20, and then
>say 80.
>Richard Rosenthal                 Internet:  richr@ai.etl.army.mil

  I think you are going to have a problem. As I remember the argument 
 from a class a few years ago: 

  One way to tile a sphere with regular (all sides/angles equal) polyhedra 
 is to take a regular solid centered at the sphere's center. Project 
 the edges of the solid onto the sphere. Works just fine. 

  The kicker is that there are only 5 known regular solids. (Not 
 counting the teapotahedron -  see CACM Feb. 1988 cover)

  If you do discover a tiling with millions of regular shapes, you 
 should be able to run the above process in reverse to create a new
 regular polyhedral solid.  

  Good luck.

 - mark