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 \({\mathbb {E}}^2\); these are the most symmetric polyhedra possible in \({\mathbb {E}}^2\). We also classify the finite 3-Orbit polyhedra with an affinely reducible symmetry group in ordinary space \({\mathbb {E}}^3\). Part II will classify the 3-Orbit polyhedra with an affinely irreducible symmetry group in \({\mathbb {E}}^3\).
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Acknowledgements
The second author was supported by PAPIIT-UNAM under project grant IN104021 and CONACYT “Fondo Sectorial de Investigación para la Educación” under grant A1-S-10839.
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Cunningham, G., Pellicer, D. Finite 3-Orbit Polyhedra in Ordinary Space I. Discrete Comput Geom 70, 1785–1819 (2023). https://doi.org/10.1007/s00454-023-00502-3
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DOI: https://doi.org/10.1007/s00454-023-00502-3