Geodesic
Euclidean realization of the product of cycles without hidden symmetries
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 777-783.

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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.
Mots-clés : quadrangulation, torus
Keywords: Cartesian product of graphs, geometric realization, symmetry group, regular polyhedron. 
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S. Lawrencenko; A. Yu. Shchikanov. Euclidean realization of the product of cycles without hidden symmetries. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 777-783. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a43/

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