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 i...

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Main Authors:	Say-Awen, April Lynne D, De Las Peñas, Ma. Louise Antonette N, Frettlöh, Dirk
Format:	text
Published:	Archīum Ateneo 2018
Subjects:	symmetry order aperiodic tilings substitution tilings rotation-invariant tilings dense tile orientations Geometry and Topology Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/16 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1015&context=mathematics-faculty-pubs
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1015
record_format	eprints
spelling	ph-ateneo-arc.mathematics-faculty-pubs-10152021-10-21T05:05:51Z Primitive substitution tilings with rotational symmetries Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk 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. 2018-07-01T07:00:00Z text application/pdf https://archium.ateneo.edu/mathematics-faculty-pubs/16 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1015&context=mathematics-faculty-pubs Mathematics Faculty Publications Archīum Ateneo symmetry order aperiodic tilings substitution tilings rotation-invariant tilings dense tile orientations Geometry and Topology Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
continent	Asia
country	Philippines Philippines
content_provider	Ateneo De Manila University Library
collection	archium.Ateneo Institutional Repository
topic	symmetry order aperiodic tilings substitution tilings rotation-invariant tilings dense tile orientations Geometry and Topology Mathematics
spellingShingle	symmetry order aperiodic tilings substitution tilings rotation-invariant tilings dense tile orientations Geometry and Topology Mathematics Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk Primitive substitution tilings with rotational symmetries
description	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.
format	text
author	Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk
author_facet	Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk
author_sort	Say-Awen, April Lynne D
title	Primitive substitution tilings with rotational symmetries
title_short	Primitive substitution tilings with rotational symmetries
title_full	Primitive substitution tilings with rotational symmetries
title_fullStr	Primitive substitution tilings with rotational symmetries
title_full_unstemmed	Primitive substitution tilings with rotational symmetries
title_sort	primitive substitution tilings with rotational symmetries
publisher	Archīum Ateneo
publishDate	2018
url	https://archium.ateneo.edu/mathematics-faculty-pubs/16 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1015&context=mathematics-faculty-pubs
_version_	1715215779965698048

Primitive substitution tilings with rotational symmetries

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