Wikipedia has a resonance structure of C60 in its "Buckminsterfullerene" item. I made a bead model with color code according to this resonance form last weekend. Again one can see the interesing pattern of this resonance structure. Also white beads (or single bonds) form a long connected one-dimensional loop.
I also tried to make another resonance structure by only paying attention to the local condition. But at the last loop, I found that I couldn't satisfy the local condition any longer. So I used a red bead to show this frustration.