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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.

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DOI (Digital Object Identifier) Link: https://doi.org/10.3390/sym4040581
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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.

Item Type: Journal Article
Copyright Holders: 2012 The Authors
ISSN: 2073-8994
Extra Information: This article belongs to the Special Issue Polyhedra
Keywords: Euclidean monotiles; aperiodicity; local rules; inflation
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 34803
Depositing User: Uwe Grimm
Date Deposited: 29 Oct 2012 16:17
Last Modified: 30 Nov 2016 11:32
URI: http://oro.open.ac.uk/id/eprint/34803
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