Equivelar Polyhedra with Few Vertices

We know that the polyhedra corresponding to the Platonic solids are equivelar. In this article we have classified completely all the simplicial equivelar polyhedra on ≤ 11 vertices. There are exactly 27 such polyhedra. For each n\geq -4 , we have classified all the (p,q) such that there exists an equivelar polyhedron of type {p,q} and of Euler characteristic n . We have also constructed five types of equivelar polyhedra of Euler characteristic -2m , for each m\geq 2 . Received February 14, 2000, and in revised form August 15, 2000. Online publication March 26, 2001.