# The Cycle Index of the Symmetry Group of the Fullerene
C_{60}

## Harald Fripertinger
^{1}

### February 19, 1996

### Abstract

Various forms, including multi-dimensional forms
of the cycle index of the symmetry group of the fullerene
C_{60} 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.

harald.fripertinger@kfunigraz.ac.at,

last changed: January 23, 2001