Re: covering a sphere with patches

> OK, I know, I forgot the octahedron...
> Then, the subdivision of the faces you obtain into smaller ones should not
> be too difficult.
>
> Jerzy Karczmarczuk
>

The triangles of a geodesic sphere e.g. subdivided icosahedron, are
not equal area though, not exactly.  Maybe exactness is not critical.

There are lots of reflections so don't have to compute a full sphere.
1/120th is a common patch to reflect around, based on rhombic
triacontahedron breaking into 4 triangles.

There's a book coming out any day now, 'Divided Spheres' by Edward
Popko that should have a lot of good info.

Kirby

http://www.amazon.com/Divided-Spheres-Geodesics-Orderly-Subdivision/dp/1466504293
> PS. People who want always have one nice mathematical formula for some
> spherical problems too often forget that it is not necessary to have two
> singularities at the poles, just one is possible with the stereographic
> projection. But the distortions are awful...
>
>
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