For a long-running project where I used the truncated icosahedron, I came to the conclusion that I could not get it to work as i wanted because the truncated icosahedron is not ‘smooth’ enough. I.e. it roles but it roles too clunky. I need a better rolling ball. After some digging on wikipedia pages, my eye fell on balls based on triangles, so-called geodesic polyhedra. This octahedron still does not roll well, obviously, but it gave me a good feel for the design of the triangles.
Notes on the design
The design is fairly straightforward. You can probably build it based on the picture above. but just in case, you can download a photo pdf here.