Primitive substitution tilings with rotational symmetries
College of Science
Mathematics and Statistics Department
Acta Crystallographica Section A: Foundations and Advances
This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six-and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented. © 2018 International Union of Crystallography.
Digitial Object Identifier (DOI)
Say-Awen, A. D., de Las Peñas, M. N., & Frettlöh, D. (2018). Primitive substitution tilings with rotational symmetries. Acta Crystallographica Section A: Foundations and Advances, 74 (4), 388-398. https://doi.org/10.1107/S2053273318006745
Symmetry (Mathematics); Aperiodic tilings; Tiling (Mathematics)