Cut-and-unfold approach to fullerene enumeration

A simple and effective approach for the enumeration of fullerene structures is proposed. The method combines the formalism of a fullerene graph cut-and-unfold onto a planar triangular lattice and a topological description of closed quasi-2D clusters. A tabulation of possible fullerene graphs Cn is given for the number of atoms 20 < or = n < or = 150.