Substitution tilings with dense tile orientations and n-fold rotational symmetry

It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n∈{2,3,4,5,6,8}. The proof for dense tile orientations uses a general result about irrationality of angles in certain parallelograms.

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Main Authors:	Frettlöh, Dirk, Say-Awen, April Lynne D, De Las Peñas, Ma. Louise Antonette N
Format:	text
Published:	Archīum Ateneo 2017
Subjects:	Tilings Aperiodic order Irrational angle Geometry and Topology Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/11 https://www.sciencedirect.com/science/article/pii/S0019357716300763
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1010
record_format	eprints
spelling	ph-ateneo-arc.mathematics-faculty-pubs-10102020-06-27T02:04:53Z Substitution tilings with dense tile orientations and n-fold rotational symmetry Frettlöh, Dirk Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n∈{2,3,4,5,6,8}. The proof for dense tile orientations uses a general result about irrationality of angles in certain parallelograms. 2017-02-01T08:00:00Z text application/pdf https://archium.ateneo.edu/mathematics-faculty-pubs/11 https://www.sciencedirect.com/science/article/pii/S0019357716300763 Mathematics Faculty Publications Archīum Ateneo Tilings Aperiodic order Irrational angle Geometry and Topology Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
country	Philippines
collection	archium.Ateneo Institutional Repository
topic	Tilings Aperiodic order Irrational angle Geometry and Topology Mathematics
spellingShingle	Tilings Aperiodic order Irrational angle Geometry and Topology Mathematics Frettlöh, Dirk Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N Substitution tilings with dense tile orientations and n-fold rotational symmetry
description	It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n∈{2,3,4,5,6,8}. The proof for dense tile orientations uses a general result about irrationality of angles in certain parallelograms.
format	text
author	Frettlöh, Dirk Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N
author_facet	Frettlöh, Dirk Say-Awen, April Lynne D De Las Peñas, Ma. Louise Antonette N
author_sort	Frettlöh, Dirk
title	Substitution tilings with dense tile orientations and n-fold rotational symmetry
title_short	Substitution tilings with dense tile orientations and n-fold rotational symmetry
title_full	Substitution tilings with dense tile orientations and n-fold rotational symmetry
title_fullStr	Substitution tilings with dense tile orientations and n-fold rotational symmetry
title_full_unstemmed	Substitution tilings with dense tile orientations and n-fold rotational symmetry
title_sort	substitution tilings with dense tile orientations and n-fold rotational symmetry
publisher	Archīum Ateneo
publishDate	2017
url	https://archium.ateneo.edu/mathematics-faculty-pubs/11 https://www.sciencedirect.com/science/article/pii/S0019357716300763
_version_	1681506692355850240

Substitution tilings with dense tile orientations and n-fold rotational symmetry

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