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On a Class of Polyhedra with Symmetrical Vertex Stars

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Abstract

The influence of the local symmetry of stars of some vertices of a closed convex polyhedron in E3 on its geometry is considered. A theorem on the complete classification of symmetric polyhedra some of whose vertices possess symmetric stars of deltoid or rhombic faces is proved. In the proof, we use so-called strongly symmetric polyhedra and the lemma on local symmetry conditions previously introduced by the author.

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Authors and Affiliations

  1. Platov South-Russian State Polytechnic University, Novocherkassk, Russia

    V. I. Subbotin

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  1. V. I. Subbotin
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Correspondence to V. I. Subbotin.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 169, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part II, 2019.

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Subbotin, V.I. On a Class of Polyhedra with Symmetrical Vertex Stars. J Math Sci 263, 436–444 (2022). https://doi.org/10.1007/s10958-022-05939-0

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  • DOI: https://doi.org/10.1007/s10958-022-05939-0

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