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 ?

Extensive information about the Polyhedra can be found at WolframAlpha. For example: http://www.wolframalpha.com/input/?i=polyhdedrondata+dodecahedron 
In Mathematica ( likely also in WA ) you can simply get the coordinates of the vertices of many polyhedra. For example with 
 PolyhedronData["Dodecahedron", "VertexCoordinates"]

