How to make a sphere-ish shape with triangle faces? I want to make an origami of a sphere, so I planned to print some net of a pentakis icosahedron, but I have a image of another sphere with more polygons:

I would like to find the net of such model (I know it will be very fun to cut).
Do you know if it has a name ?

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). 
