As I mentioned before, two chemists, Vukicevic and Randic, gave a complete enumeration of all possible resonance forms in their paper, Detailed Atlas of Kekulé Structures of the Buckminsterfullerene, in "The Mathematics and Topology of Fullerenes". According to them, there are 158 irreducible Kekule structures for C60. Following the Schlegel diagrams listed in the paper, one can easily make a bead model for any resonance structure.
I found these two intriguing resonance forms, No. 108 and 111, of C60 quite accidentally yesterday. Although I knew the existence of No. 108 for a long time, I didn't know No. 111 before. I also suspect they might be the only two resonance structures which have patterns of parallel stripes along the latitude coordinates. Particularly, the Kekule structure 108 has a 5-fold rotational symmetry axis with two pentagons located at two poles and the Kekule structure 111 has a 3-fold rotational symmetry instead.