I spent some time exploring ways to mutate the Buckyball using Stone Wales transformations. Here is an interesting one:
Instead of 20 hexagons it has 10 heptagons and 10 extra pentagons, so it has 22 pentagons and 10 heptagons.
22+10 = 32 = 12+20: With these transformations, the number of vertices, edges and faces remains invariant. Also the valence of each vertex stays invariant. The sides per polygon changes, incrementing 2 while decrementing 2 others.
