Why not

I have actually had want for these at times and needed to resort to manually constructing them from a ridiculously large number of prims!
Set the number of faces and use a standard geodesic algorithm to calculate the shape for general geodesics, including the Icosahedron (20 sides). Use invalid #_of_faces values to flag Dodecahedron (12 pentagonal sides), and Truncated Icosahedron (soccer ball - 32 sides, 12 pentagon, 20 hexagon) shapes as special cases.
Would be treated like spheres in the editor, with dimple and cut rounded to take out whole faces at a time?
Probably treat as faceted spheres in the Physics engine too.