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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 99–127
(Mi tm3344)
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This article is cited in 1 scientific paper (total in 1 paper)
On the enumeration of Archimedean polyhedra in the Lobachevsky space
V. S. Makarova, P. V. Makarovb a M. V. Lomonosov Moscow State University, Moscow, Russia
b Moscow State Mining University, Moscow, Russia
Abstract:
We describe the class of Archimedean polyhedra in the three-dimensional Lobachevsky space, which technically reduces to studying Archimedean tilings of the Lobachevsky plane. We analyze the possibility of obtaining Archimedean tilings by methods that are usually applied on the sphere and in the Euclidean plane. It is pointed out that such tilings can be constructed by using certain types of Fedorov groups in the Lobachevsky plane. We propose a general approach to the problem of classifying Archimedean tilings of the Lobachevsky plane.
Received in September 2010
Citation:
V. S. Makarov, P. V. Makarov, “On the enumeration of Archimedean polyhedra in the Lobachevsky space”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 99–127; Proc. Steklov Inst. Math., 275 (2011), 90–117
Linking options:
https://www.mathnet.ru/eng/tm3344 https://www.mathnet.ru/eng/tm/v275/p99
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Abstract page: | 351 | Full-text PDF : | 151 | References: | 93 |
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