Two-orbit polyhedra from groups

Abstract polytopes are combinatorial structures that generalize the classical notion of convex polytopes. In this paper particular attention is given to polytopes whose automorphism groups (or groups of symmetries) have exactly two orbits on the set of flags. Two-orbit polytopes of rank n are classified in terms of their local configuration of flags. Furthermore, a characterization of two-orbit polyhedra in terms of their automorphism group is given; that is, necessary and sufficient conditions for a group to be the automorphism group of a two-orbit polyhedron are found.