Distance on the Cairo pattern

Abstract

The Cairo pattern is a dual of a semiregular tiling of the plane; its name reflects the fact that various streets in Cairo are paved in this way. The cells of this grid are identical pentagons which are put in four different orientations. In this paper we present a coordinate system addressing the cells of the grid. Also a neighborhood relation and the concept of lanes are defined by the help of the coordinates. We prove a formula for the digital (path based) distance between any two pentagons where the paths are based on the steps to neighbor pentagons. (c) 2021 Elsevier B.V. All rights reserved.