Construction of the discrete hull for the combinatorics of a regular\n pentagonal tiling of the plane

2013/03/21 by Maria Ramirez-Solano, Ramirez-Solano, Maria
Computer Science · Materials Science · #46L55 #52C20 #52C26 #Cellular Automata and Applications #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1303.5375

openalex publication_date 2013/03/21 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

The article 'A "regular" pentagonal tiling of the plane' by P. L. Bowers and\nK. Stephenson defines a conformal pentagonal tiling. This is a tiling of the\nplane with remarkable combinatorial and geometric properties. However, it\ndoesn't have finite local complexity in any usual sense, and therefore we\ncannot study it with the usual tiling theory. The appeal of the tiling is that\nall the tiles are conformally regular pentagons. But conformal maps are not\nallowable under finite local complexity. On the other hand, the tiling can be\ndescribed completely by its combinatorial data, which rather automatically has\nfinite local complexity. In this paper we give a construction of the discrete\nhull just from the combinatorial data. The main result of this paper is that\nthe discrete hull is a Cantor space.\n

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