Symmetry 2012, 4(4), 581-602; doi:10.3390/sym4040581
Article

Hexagonal Inflation Tilings and Planar Monotiles

Received: 2 September 2012; in revised form: 8 October 2012 / Accepted: 14 October 2012 / Published: 22 October 2012
(This article belongs to the Special Issue Polyhedra)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 focused 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.
Keywords: Euclidean monotiles; aperiodicity; local rules; inflation
PDF Full-text Download PDF Full-Text [452 KB, Updated Version, uploaded 30 November 2012 15:20 CET]
The original version is still available [452 KB, uploaded 22 October 2012 16:37 CEST]

Export to BibTeX |
EndNote


MDPI and ACS Style

Baake, M.; Gähler, F.; Grimm, U. Hexagonal Inflation Tilings and Planar Monotiles. Symmetry 2012, 4, 581-602.

AMA Style

Baake M, Gähler F, Grimm U. Hexagonal Inflation Tilings and Planar Monotiles. Symmetry. 2012; 4(4):581-602.

Chicago/Turabian Style

Baake, Michael; Gähler, Franz; Grimm, Uwe. 2012. "Hexagonal Inflation Tilings and Planar Monotiles." Symmetry 4, no. 4: 581-602.

Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert