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
Brazil

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

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

Abstract:

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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