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Primitive substitution tilings with rotational symmetries

Primitive substitution tilings with rotational symmetries 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

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References (16)

Publisher
Wiley
Copyright
Copyright © 2018 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S2053273318006745
pmid
29978848
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Crystallographica Section A Foundations of CrystallographyWiley

Published: Jul 1, 2018

Keywords: ; ; ; ;

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