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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, Number 2, Pages 74–84 (Mi basm475)  

Research articles

Isohedral tilings by $8$-, $10$- and $12$-gons for hyperbolic translation group of genus two

Elizaveta Zamorzaeva

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

Abstract: As is known there are 2 types of isoheral tilings of the Euclidean plane with disks for the translation group $p1$. In the hyperbolic plane there exist a countable series of translation groups, each group being characterized by its genus. For the hyperbolic translation group of genus two, isohedral tilings of the hyperbolic plane with disks are studied. The technique of adjacency symbols, developed by B. N. Delone for the Euclidean case, is used. In the present article we restrict the enumeration to tilings with $8$-, $10$- and $12$-gons.

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

Funding Agency Grant Number
SCSTD 12.839.08.07F
SCSTD 15.817.02.26F
The work was partially supported by the SCSTD Projects 12.839.08.07F and 15.817.02.26F.


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Document Type: Article
MSC: Primary 52C20; Secondary 05B45
Received: 18.03.2018
Language: English

Citation: Elizaveta Zamorzaeva, “Isohedral tilings by $8$-, $10$- and $12$-gons for hyperbolic translation group of genus two”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 2, 74–84

Citation in format AMSBIB
\Bibitem{Zam18}
\by Elizaveta~Zamorzaeva
\paper Isohedral tilings by $8$-, $10$- and $12$-gons for hyperbolic translation group of genus two
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2018
\issue 2
\pages 74--84
\mathnet{http://mi.mathnet.ru/basm475}


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  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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