Penrose tilings as coverings of congruent decagons
type: Item
instance of: scholarly article
title: Penrose tilings as coverings of congruent decagons
zbMATH Open document ID: 0893.52011
DOI: 10.1007/BF00239998
author: Petra Gummelt
published in: Geometriae Dedicata
publication date: 1998-08-04T00:00:00Z
review text: The Penrose tilings show that there is a set of two prototiles, with which the Euclidean plane can be tiled, but only in a nonperiodic way. Is there a set of first one prototile with the same property? This problem remains open; but there the author solves the analogous problem for covering: A regular decagon can serve as a single proto``tile''. To cover the Euclidean plane some decagons will of course overlap. These overlaps are however governed by matching rules: The proto``tile'' consists of white and dark regions, and we require that all dark regions are overlapped, and that colours match. Since the colouring of the regions is based on Penrose tilings, the ``tiling'' is necessarily nonperiodic.
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 82D25
zbMATH DE Number: 929904
zbMATH Keywords: covering
zbMATH Keywords: aperiodic tile
zbMATH Keywords: quasicrystal
zbMATH Keywords: Penrose tilings
reviewed by: Jonathan Schaer
Wikidata QID: Q60728950
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 929904