Regular tessellation of the Lobachevskii plane - P.I. Troshin (Учёные записки Казанского университета: Серия Физико-математические науки)
This paper discusses a new algorithm for construction of regular tessellation of the Lobachevskii plane. The problems of combinatorial and topological arrangement of regular tessellations, finding the number of tiles in each layer of such tessellation, and implementation of the algorithm in the modern computer programming language were studied. The relevance of the study is determined, on the one hand, by the unceasing interest in hyperbolic geometry and, in particular, in tessellations within it. On the other hand, the relevance is due to the insufficient number of published algorithm descriptions and their implementations. The following methods were used: