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IMI/Publicaţii/BASM/Ediţii/BASM n.1(89), 2019/

Isohedral tilings by 14-, 16- and 18-gons for hyperbolic translation group of genus two

Authors: Elizaveta Zamorzaeva

Abstract

There are 2 types of isohedral tilings of the Euclidean plane with disks for the translation group $p1$. In the hyperbolic plane there exist countably many translation groups, each translation group is characterized by its genus. The present article continues work [7] and studies isohedral tilings of the hyperbolic plane with disks for the translation group of genus two. We use the technique of adjacency symbols, developed by B.~N.~Delone for the Euclidean plane. In [7] isohedral tilings of the hyperbolic plane with 8-, 10- and 12-gons were obtained. In the present article isohedral tilings of the hyperbolic plane with 14-, 16- and 18-gons are obtained, thus completing the enumeration.

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