How to make a sphere-ish shape with triangle faces?

Here is a net of a buckyball, from GoldenNumber.net:

It should be possible to turn this into the kind of net you're looking for by replacing the pentagons and hexagons with 5 and 6 isosceles triangles (the heights of the triangles determine the "elevation" of the center vertex from the original pentagonal/hexagonal faces and thus affect the sphericality of the result).

This whitepaper on Geodesic Math may be helpful.

Probably less helpful is this Ruby Quiz I hosted on writing a program to calculate Geodesic spheres.