Closed-shell three-connected clusters: topological and group-theoretical aspects

Abstract

Group-theoretical and topological arguments are presented within the tensor surface harmonic framework in order to predict polyhedral geometries for three-connected pseudo-spherical clusters, such as the C_2n fullerenes. Topological and symmetry relationships between polyhedra, their duals, edge-figures and truncated derivatives are outlined. A general way of generating closed-shell three-connected cluster geometries, by polyhedral truncation, is presented. Finally, group-theoretical and topological aspects of alternancy in three-dimensional clusters are discussed.