Remarks on 2-dimensional quasiperiodic tilings with rotational symmetries
type: Item
instance of: scholarly article
title: Remarks on 2-dimensional quasiperiodic tilings with rotational symmetries
zbMATH Open document ID: 1175.52026
author: Kazuhisa Kato
author: Kazushi Komatsu
author: Fumihiko Nakano
author: Kentaro Nomakuchi
author: Masatetsu Yamauchi
published in: Hiroshima Mathematical Journal
publication date: 2009-04-21T00:00:00Z
review text: A sequentially compact space of patches is constructed. Using this construction it is proved: Let \(S\) be a prototile set with a substitution rule \(\Phi\). If we have a prototile with a vertex of an angle \(\pi/n\), then there exists a tiling \(T_n\) with \(n\)-fold rotational symmetry, which is a periodic point of \(\widehat\Phi\). Furthermore, for an integer \(n\) with \(n= 5\) or \(6< n\), its tiling \(T_n\) is nonperiodic and has non-trivial action of a non-crystallographic Coxeter group.
reviewed by: Milica Stojanović
Mathematics Subject Classification ID: 52C23
Mathematics Subject Classification ID: 52C20
zbMATH DE Number: 5545480
zbMATH Keywords: quasiperiodic tiling
zbMATH Keywords: substitutional rule
zbMATH Keywords: rotational symmetry
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1233152776
OpenAlex ID: W1489205363
Wikidata QID: Q128872335
DOI: 10.32917/HMJ/1233152776
description: scientific article; zbMATH DE number 5545480