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

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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 ?

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3 Answers

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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.

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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).

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Extensive information about the Polyhedra can be found at WolframAlpha. For example:

In Mathematica ( likely also in WA ) you can simply get the coordinates of the vertices of many polyhedra. For example with

 PolyhedronData["Dodecahedron", "VertexCoordinates"]

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