Here is a graphic I drew with an earlier version of Mathematic (probably version 6) which I no longer have available:
At the time
Polyhedra was an external package, and I produced the cut-away by truncating a list of component polyhedra of the truncated icosahedron before drawing.
Recent versions of Mathematica have an entirely different (and now integrated) set of polyhedron functions, that look nothing like what I used before. Can anyone suggest a strategy for redrawing this figure now?