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JOURNALS // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Archive

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019 Number 1, Pages 91–102 (Mi basm495)

This article is cited in 1 paper

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

Elizaveta Zamorzaeva

Moldova State University, 60 Mateevici str., Chisinau, MD-2009, Republic of Moldova

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.

Keywords and phrases: isohedral tiling, hyperbolic plane, translation group of genus two, Delone class, adjacency symbol.

MSC: Primary 52C20; Secondary 05B45

Received: 23.01.2019

Language: English



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