Fullerene Symmetries and Coxeter Groups Approach

Maia Angelova

maia.angelova@unn.ac.uk

School of Computing and Mathematics University of Northumbria at Newcastle

Abstract

Fullerenes, C_{n}, are all-carbon molecules with a closed-cage structure and a nearly spherical appearance. Each carbon atom is bonded to three others to form a polyhedron with 12 pentagonal and (\frac{1}{2}n − 10) hexagonal faces. The best known fullerene is C_{60}, the molecule with 60 equivalent carbon atoms arranged on the vertices of a truncated icosahedron. The properties of C_{60} molecule are discussed and its icosahedral symmetry is described. Finite Coxeter groups H_{3} and H_{4} and their Coxeter diagrams are introduced and the symmetry of C_{60} fullerene is illustrated by the diagrams of the group H_{3}. The solid form of C_{60} is described, some interesting doped structures are given and their properties discussed. The symmetries of other popular fullerenes are also considered. Possible embedding of fullerenes to form onionlike structures are discussed and illustrated by the groups H_{3} and H_{4}.

Special knowledge of the matter is not required. All structures would be illustrated in details and all necessary definitions given. The talk would be accessible to a broad audience.