Labyrinth on a buckyball

Using the idea I introduced in the previous post, we can create 2²⁰/20 different patterns of labyrinth for C60! The basic idea is to start from the original VB pattern with icosahedral symmetry which I will call the canonical VB structure. Each of 20 hexagons on C60 has two local Kekule structures. We can apply a six-fold rotation to switch them from one to another. In total, we have 2²⁰/20 possibilities. But there are still many over-countings. Working out all distinct VB structures is a nontrivial combinatorial problem. Possibly someone has already done it.

Right now, I only have one additional colored beaded C60 with only one local Kekule structure rotated into another resonance form. One can see the curious local 3-fold pattern (3-fold leaf). I will make another bead model of C60 with four local Kekule structures rotated and create four non-overlapping 3-fold leafs, or a tiling on sphere with four 3-fold leafs.