Two steps forward, one step back...

Decided to set aside the sphere generation algorithm I'd come up with,
and try a different one.

This new one uses recursion to produce a sort of fractal geometry, which
I suspect is similar to the way that Google Earth handles this problem.

Incidentally, it looks like this approach may actually require fewer
lines of code.
Oops...

Reversed the order of the vertices going into the triangles, so that the
normals come out right.