Regular Polyhedra of Index Two, I - Mathematics > Metric GeometryReport as inadecuate




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Abstract: A polyhedron in Euclidean 3-space is called a regular polyhedron of index 2if it is combinatorially regular but -fails geometric regularity by a factor of2-; its combinatorial automorphism group is flag-transitive but its geometricsymmetry group has two flag orbits. The present paper, and its successor by thefirst author, describe a complete classification of regular polyhedra of index2 in 3-space. In particular, the present paper enumerates the regular polyhedraof index 2 with vertices on two orbits under the symmetry group. The subsequentpaper will enumerate the regular polyhedra of index 2 with vertices on oneorbit under the symmetry group.



Author: Anthony M. Cutler, Egon Schulte

Source: https://arxiv.org/







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