The uniform locally finite tilings of the plane
type: Item
instance of: scholarly article
title: The uniform locally finite tilings of the plane
zbMATH Open document ID: 1151.52014
published in: Journal of Combinatorial Theory. Series B
publication date: 2008-07-24T00:00:00Z
review text: The uniform locally finite tilings of the plane by finite combinatorial objects called labeling schemes are characterized. This representation is based on the analysis of the group of symmetries of a tiling which is realized independently of its geometry. It is shown that such tilings can be embedded in a geometry of the plane such that all tiles are regular polygons. As a consequence, it is given enumeration of all the uniform locally finite tilings having a given internal degree. It is also possible to decide whether or not there exists a tiling possessing a particular local geometric property.
reviewed by: Milica Stojanović
Mathematics Subject Classification ID: 52C20
zbMATH DE Number: 5303720
zbMATH Keywords: tiling of the plane
zbMATH Keywords: isogonal tiling
zbMATH Keywords: Fuchsian group
zbMATH Keywords: group of symmetries
zbMATH Keywords: locally finite
zbMATH Keywords: labeling scheme
author: David Renault
MaRDI profile type: Publication
full work available at URL: j.jctb.2007.10.003
OpenAlex ID: W2087601490
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DOI: 10.1016/J.JCTB.2007.10.003
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description: scientific article; zbMATH DE number 5303720