The Cycle Indices of the Symmetry Groups of Fullerenes

Harald Fripertinger 1

Lecture given at the 38. Séminaire Lotharingien de Combinatoire in Bellagio, from October 6, to October 9, 1996.


Various forms, including multi-dimensional forms of the cycle index of the symmetry group of the fullerene C60 acting on its sets of vertices, faces, edges etc. are computed and applied for the enumeration of essentially different colourings of the truncated icosahedron. Furthermore we determine the 3-dimensional cycle index of a polyhedron under the leapfrog operation introduced by P.W. Fowler.

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