Three Kekule structures of C60

D. Vukicevic and M. Randic have figured out all possible distinct resonance (or Kekule) structures a few years ago. According them, buckminsterfullerene has 12500 Kekule structures grouped in 158 isomorphic classes. They also give a complete list of all these 158 non-isomorphic Kekuke structures in a recent paper entitled "Detailed Atlas of Kekulé Structures of the Buckminsterfullerene", in the book, "The Mathematics and Topology of Fullerenes".

This is very convenient if we want to make any particular resonance form of C₆₀. We can simply look at the Schlegel diagrams given in this paper, and pay attention to the single and double bond pattern as we bead. Here are three bead models for Kekule structures No. 134, 135 and 136 as shown in their paper.