Hexagonal inflation tilings and planar monotiles

Baake, Michael; Gähler, Franz and Grimm, Uwe (2012). Hexagonal inflation tilings and planar monotiles. Symmetry, 4(4) pp. 581–602.

DOI: https://doi.org/10.3390/sym4040581

Abstract

Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography. In this direction, many people have tried to construct aperiodic tilings that are built from a single prototile with nearest neighbour matching rules, which is then called a monotile. One strand of the search for a planar monotile has focussed on hexagonal analogues of Wang tiles. This led to two inflation tilings with interesting structural details. Both possess aperiodic local rules that define hulls with a model set structure. We review them in comparison, and clarify their relation with the classic half-hex tiling. In particular, we formulate various known results in a more comparative way, and augment them with some new results on the geometry and the topology of the underlying tiling spaces.

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About

• Item ORO ID
• 34803
• Item Type
• Journal Item
• ISSN
• 2073-8994
• Extra Information
• This article belongs to the Special Issue Polyhedra
• Keywords
• Euclidean monotiles; aperiodicity; local rules; inflation
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2012 The Authors
• Depositing User
• Uwe Grimm