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From: bdiscoe@tybalt.caltech.edu (Ben W. Discoe)
Newsgroups: comp.graphics
Subject: Re: Tesselating the sphere
Message-ID: <1990Feb24.070934.4605@spectre.ccsf.caltech.edu>
Date: 24 Feb 90 07:09:34 GMT
References: <155@tacitus.tfic.bc.ca> <271@dg.dg.com>
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Organization: California Institute of Technology
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mpogue@dg.dg.com (Mike Pogue) writes:

>  It so happens that I am working on this right now (in my copious spare time).
>The geometry is well-known, and has been used by good ole Bucky Fuller for 
>quite a few years.

I have searched Bucky's books for any sign of REAL mathematics or useable
formulas and remain empty-handed.  The method of raising polyhedra to
higher frequencies is not at all well-known, in fact I have access to
extensive geometry/computer sciece media and have not found ANY instances
of theory/code anywhere.  I finally stumbled across a formula for distance
along a geodesic between any two points, but still have no formula for the
arc itself (necessary for adding the intermediary points -> frequency).
If ANYONE on the net knows of such formula/algorithms I would be MOST
grateful...

>You can also start with an icosahedron, and you get a better approximation, but
>structurally it acts quite different (I'm interested from the geodesic dome
>point of view).

I am also interested in the dome point of view...  I asked for help in this
group some months back and received no solid answers.  Apparently we
geodesic-types are few and far between in a cubical world.

>  I have ray traced a 4-frequency octahedron, which looks quite nice...
> Icosahedron
>is a bit more complex, having a more complicated arrangement of sides.

Is it correct that a unit-edge-length tetrahedron's radius is slightly less
than one?  I think if it were 1.0 then it would be a "vector equilibrium."
Sounds like you have running code - are you free to distribute it?

>Mike Pogue
>I speak for myself, not my company....

-Ben Discoe "Every 3 months we throw away enough aluminum to rebuild our
		commercial airfleet."