Type: Article

Finite 3-orbit polyhedra in ordinary space I

Cunningham, Gabe; Pellicer, Daniel;

Abstract:

We study polyhedra in the skeletal sense, where faces consist of merely a frame without any membrane. A 3-Orbit polyhedron is one where the symmetry group has three orbits on the flags. Prisms, bipyramids, and truncations of regular polyhedra are all examples of 3-Orbit polyhedra. In this paper we classify the finite 3-Orbit polyhedra in the plane ; these are the most symmetric polyhedra possible in . We also classify the finite 3-Orbit polyhedra with an affinely reducible symmetry group in ordinary space . Part II will classify the 3-Orbit polyhedra with an affinely irreducible symmetry group in .