The Cycle Index of the Symmetry Group of the Fullerene C₆₀

Harald Fripertinger ¹

February 19, 1996

Abstract

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. The implementation of these cycle index methods in the computer algebra system SYMMETRICA is discussed, and finally cycle indices of the symmetry groups of some further fullerenes are derived.