More icosahedral fulleroids

The discovery of the famous fullerene has raised an interest in the study o f other candidates for a modeling of carbon molecules. Motivated by a P. Fo wler's question Delgado Friedrichs and Deza defined I (a, b)-fulleroids as cubic convex polyhedra having only a-gonal and b-gonal faces and the symmet ry groups isomorphic with the rotation group of the regular icosahedron. In this note we prove that for every n greater than or equal to 8 there exist infinitely many 1(5, n)-fulleroids. This answers positively questions pose d recently by Delgado Friedrichs and Deza.