Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!samsung!emory!hubcap!jhanks
From: jhanks@hubcap.clemson.edu (Jim Hanks)
Newsgroups: comp.theory.cell-automata
Subject: Re: Spherical CA
Message-ID: <10791@hubcap.clemson.edu>
Date: 5 Oct 90 14:23:09 GMT
References: <90277.175712HFIHC@CUNYVM.BITNET> <1990Oct5.064458.26401@uniwa.uwa.oz>
Organization: Clemson University, Clemson, SC
Lines: 30

tim@maths.uwa.oz.au (Tim Boykett) writes:

>HFIHC@CUNYVM writes:

>>Has anyone ever designed and/or implemented a CA for a spherical surface?

>You will need to use shapes that are polyhedra, ie they are
>topologically isomorphic to a sphere, but they have flat surfaces. 

>what these look like in any role-playing game shop, the are dice
>with 4,8,20 sides resp. With square faces, you can only get a cube
>shape, with pentagons you can only get a 12-sided shape.
>  I don't think there are anyother regular polyhedra that can be made
>though  have a weak memory of someone shoing me a 100-sided dice
>that was regular.

You are correct in saying that that are no other regular polyhedra other
than the tetrahedron, cube, octahedron, dodecahedron, and icosahedron
(4,6,8,12,and 20 faces respectively).  However there are other solids
which are not regular but which have identical faces.  For example, I
have seen a 30-sided figure whose sides were rhombuses (diamonds). This
solid is not regular but as each face has four neighbors, may be useful
as a base for a "spherical" CA.  In fact, I remember a book which had a
whole slew of solids like this, but I can't remember the name :(.
Something like "Mathematical Models".  Hope this helps


jhanks@hubcap.clemson.edu
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