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.

- Introduction
- Some cycle indices
- Some counting problems
- A multi-dimensional cycle index
- Implementation in SYMMETRICA
- Some further fullerenes
- Some numerical examples using SYMMETRICA
- References
- Address of the author
- Footnotes

harald.fripertinger "at" uni-graz.at, May 10, 2016