2010/11/12 by Cutler, Anthony M.
#Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Primary: 51M20. Secondary: 52B15
paper · doi:10.48550/arxiv.1011.3034
A polyhedron in Euclidean 3-space is called a regular polyhedron of index 2 if it is combinatorially regular and its geometric symmetry group has index 2 in its combinatorial automorphism group; thus its automorphism group is flag-transitive but its symmetry group has two flag orbits. The present paper completes the classification of finite regular polyhedra of index 2 in 3-space. In particular, this paper enumerates the regular polyhedra of index 2 with vertices on one orbit under the symmetry group. There are ten such polyhedra.