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Regular polyhedra of index two, II

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Abstract

A polyhedron in Euclidean 3-space \({{\mathbb{E}^3}}\) 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 \({{\mathbb{E}^3}}\) . 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.

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  1. Northeastern University, Boston, MA, 02115, USA

    Anthony M. Cutler

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  1. Anthony M. Cutler
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Cutler, A.M. Regular polyhedra of index two, II. Beitr Algebra Geom 52, 357–387 (2011). https://doi.org/10.1007/s13366-011-0022-1

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