After doing my icosahedron study, I wanted to do another one for the truncated icosahedron (you know, the soccer ball/buckyball/nuclear bomb poly).
Thinking about it and looking at the math, I was struck by the pattern of the vertex permutations. I wanted to retain some of that in my program because it was interesting (and I hate working with tables of seemingly meaningless numbers).
When I was done, I realized that the app could easily be tweaked to accommodate most of the other polyhedrons. So I did.