The problem of the generation of polyhedra with degree3 vertices, and faces each of which is pentagonal or hexagonal, is addressed in order to characterize carbon in order to characterize clusters of ca. 30 or more atoms. Following Eulerian type arguments such polyhedra are subcategorized in terms of numbers of different types of local structures. An algorithm to generate such polyhedra is developed, and its computer implementation is described. Results for smaller than 80vertex cages of subcategories anticipated to be more chemically relevant are reported. The singular position of the truncatedicosahedron (buckminsterfullerene) structure is noted. Copyright 1991 John Wiley & Sons, Inc.
