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Primitive substitution tilings with rotational symmetries
Author(s) -
Say-awen April Lynne D.,
De Las Peñas Ma. Louise Antonette N.,
Frettlöh Dirk
Publication year - 2018
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273318006745
Subject(s) - substitution (logic) , homogeneous space , substitution tiling , crystallography , combinatorics , physics , mathematics , geometry , chemistry , computer science , programming language
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 σ 6 and σ 7 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.