Journal of Integer Sequences, Vol. 20 (2017), Article 17.10.6

Enumeration of Vertices, Edges and Polygons in Tessellations of the Plane

Marcelo Firer
Imecc — Unicamp
Rua Sérgio Buarque de Holanda 651
13083-859 Campinas — SP

Karine Bobadilha Couto
Fatec — Catanduva
Rua Maranhão 898
15800-020 Catanduva — SP

Eduardo Brandani da Silva
Department of Mathematics
Maringa State University
Av. Colombo
5790 Maringa, PR


In this work, we consider the tessellations (or tilings) of Euclidean and hyperbolic planes using copies of a regular polygon. We introduce the concept of k-type of vertices and edges, which allow a thorough control of these elements when the tessellation increases, and we obtain an enumeration for the vertices, edges, and polygons at a given distance.

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Received January 26 2016; revised versions received August 7 2017; September 9 2017; November 18 2017. Published in Journal of Integer Sequences, November 19 2017.

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