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sphere tesselation with Mathematica

I was wondering if I can solve the following problem easily with
Mathematica. I am trying to represent a sphere as a number of
equidistantly spaced points on its surface (i.e., if you can fold open
the sphere without any distortions, the points will be hexagonally
"close" packed)?  Specifically, I am trying to represent the surface of
a sphere as a collection of identical equilateral triangles.



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