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Abstract: The discovery of the fullerene has raised an interest in the study of other candidates for modeling of carbon molecules. Motivated by works of P.~Fowler, Delgado Friedrichs and Deza, $O_h(a,b)$-fulleroids were defined as cubic convex polyhedra having only $a$-gonal and $b$-gonal faces and the symmetry group isomorphic with the full symmetry group of regular octahedron. In this paper we give sufficient and necessary condition for existence of $O_h(5,n)$-fulleroids depending on number $n$ either by finding infinite series of examples to prove existence or proving nonexistence using symmetry invariants. Contact the authors: kardos@science.upjs.sk, jendrol@kosice.upjs.sk Download PDF version of the preprint. |