Hexagonal Inflation Tilings and Planar Monotiles

Baake M, Gähler F, Grimm U (2012)
Symmetry 4(4): 581-602.

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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 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.
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Article Processing Charge funded by the Deutsche Forschungsgemeinschaft and the Open Access Publication Fund of Bielefeld University.
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Baake M, Gähler F, Grimm U. Hexagonal Inflation Tilings and Planar Monotiles. Symmetry. 2012;4(4):581-602.
Baake, M., Gähler, F., & Grimm, U. (2012). Hexagonal Inflation Tilings and Planar Monotiles. Symmetry, 4(4), 581-602.
Baake, M., Gähler, F., and Grimm, U. (2012). Hexagonal Inflation Tilings and Planar Monotiles. Symmetry 4, 581-602.
Baake, M., Gähler, F., & Grimm, U., 2012. Hexagonal Inflation Tilings and Planar Monotiles. Symmetry, 4(4), p 581-602.
M. Baake, F. Gähler, and U. Grimm, “Hexagonal Inflation Tilings and Planar Monotiles”, Symmetry, vol. 4, 2012, pp. 581-602.
Baake, M., Gähler, F., Grimm, U.: Hexagonal Inflation Tilings and Planar Monotiles. Symmetry. 4, 581-602 (2012).
Baake, Michael, Gähler, Franz, and Grimm, Uwe. “Hexagonal Inflation Tilings and Planar Monotiles”. Symmetry 4.4 (2012): 581-602.
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