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This article is cited in 1 scientific paper (total in 1 paper)
Geometry and topology
Euclidean realization of the product of cycles without hidden symmetries
S. Lawrencenkoa, A. Yu. Shchikanovb a Russian State University of Tourism and Service, ul. Glavnaya, 99, 141221, Cherkizovo, Pushkino District, Moscow Region, Russia
b University of Technology, ul. Gagarin, 42, 141070, Korolev, Moscow Region, Russia
Abstract:
It is shown that any graph G that is the Cartesian product of two cycles can be realized in four-dimensional Euclidean space in such a way that every edge-preserving permutation of the vertices of G extends to a symmetry of the Euclidean realization of G. As a corollary, there exists an infinite series of regular toroidal two-dimensional polyhedra inscribed in the Clifford torus just like the five regular spherical polyhedra are inscribed in a sphere.
Keywords:
quadrangulation, torus, Cartesian product of graphs, geometric realization, symmetry group, regular polyhedron.
Received April 10, 2015, published November 5, 2015
Citation:
S. Lawrencenko, A. Yu. Shchikanov, “Euclidean realization of the product of cycles without hidden symmetries”, Sib. Èlektron. Mat. Izv., 12 (2015), 777–783
Linking options:
https://www.mathnet.ru/eng/semr626 https://www.mathnet.ru/eng/semr/v12/p777
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Abstract page: | 229 | Full-text PDF : | 63 | References: | 44 |
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