The thing that bothers me about most sphere approximations by
subdivision is that they are typically geared towards keeping the
triangles as close to equilateral as possible, while for some
applications it may be more important to aim for triangles of uniform
size (or, more precisely, for triangles corresponding to uniform solid
angles).

To that end, I suspect a pentakis dodecahedron (aka kisdodecahedron; a
dodecahedron with each face split up into five triangles, for a total of
60 triangles) might be a better starting point.

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