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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2015_12_a43,
     author = {S. Lawrencenko and A. Yu. Shchikanov},
     title = {Euclidean realization of the product of cycles without hidden symmetries},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {777--783},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a43/}
}
TY  - JOUR
AU  - S. Lawrencenko
AU  - A. Yu. Shchikanov
TI  - Euclidean realization of the product of cycles without hidden symmetries
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 777
EP  - 783
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a43/
LA  - ru
ID  - SEMR_2015_12_a43
ER  - 
%0 Journal Article
%A S. Lawrencenko
%A A. Yu. Shchikanov
%T Euclidean realization of the product of cycles without hidden symmetries
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 777-783
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a43/
%G ru
%F SEMR_2015_12_a43
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/