Shield tilings

Document Type : Research Paper

Authors

1 HSE University, Moscow, Russia

2 Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia

Abstract

We provide a complete description of the edge-to-edge tilings with a regular triangle and a shield-shaped hexagon with no right angle. The case of a hexagon with a right angle is also briefly discussed.

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References

[1] H. Cohn, R. Kenyon and J. Propp, A variational principle for domino tilings, Journal of the American Mathematical Society, 14 (2001) 297–346.
[2] Th. Fernique, A. Hashemi and O. Sizova, Compact packings of the plane with three sizes of discs, Discrete and Computational Geometry, 66 (2021) 613–635.
[3] F. Gähler, Crystallography of dodecagonal quasicrystals, Universitätsbibliothek der Universität Stuttgart, 2009.
[4] M. Impe´ror-Clerc, A. Jagannathan, P. Kalugin and J.-F. Sadoc, Square-triangle tilings: an infinite playground for soft matter, Soft Matter, 17 (2021) 9560–9575.
[5] Th. Kennedy, Compact packings of the plane with two sizes of discs, Discrete and Computational Geometry, 35 (2006) 255–267.
[6] M. Oxborrow and Ch. L. Henley, Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals, Physical Review B, 48 (1993) 6966–6998.

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History

  • Receive Date: 04 July 2023
  • Revise Date: 09 January 2024
  • Accept Date: 10 January 2024
  • Published Online: 23 January 2024

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