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Unification and classification of two-dimensional crystalline patterns using orbifolds

Hyde, Stephen; Ramsden, Stuart; Robins, Vanessa

Description

The concept of an orbifold is particularly suited to classification and enumeration of crystalline groups in the euclidean (flat) plane and its elliptic and hyperbolic counterparts. Using Conway's orbifold naming scheme, this article explicates conventional point, frieze and plane groups, and describes the advantages of the orbifold approach, which relies on simple rules for calculating the orbifold topology. The article proposes a simple taxonomy of orbifolds into seven classes, distinguished...[Show more]

dc.contributor.authorHyde, Stephen
dc.contributor.authorRamsden, Stuart
dc.contributor.authorRobins, Vanessa
dc.date.accessioned2015-12-13T22:30:43Z
dc.identifier.issn0108-7673
dc.identifier.urihttp://hdl.handle.net/1885/74967
dc.description.abstractThe concept of an orbifold is particularly suited to classification and enumeration of crystalline groups in the euclidean (flat) plane and its elliptic and hyperbolic counterparts. Using Conway's orbifold naming scheme, this article explicates conventional point, frieze and plane groups, and describes the advantages of the orbifold approach, which relies on simple rules for calculating the orbifold topology. The article proposes a simple taxonomy of orbifolds into seven classes, distinguished by their underlying topological connectedness, boundedness and orientability. Simpler 'crystallographic hyperbolic groups' are listed, namely groups that result from hyperbolic sponge-like sections through three-dimensional euclidean space related to all known genus-three triply periodic minimal surfaces (i.e. the P, D, Gyroid, CLP and H surfaces) as well as the genus-four I-WP surface.
dc.publisherMunksgaard International Publishers
dc.rightsAuthor/s retain copyright
dc.sourceActa Crystallographica Section A: Foundations of Crystallography
dc.titleUnification and classification of two-dimensional crystalline patterns using orbifolds
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume70
dc.date.issued2014
local.identifier.absfor010200 - APPLIED MATHEMATICS
local.identifier.absfor020400 - CONDENSED MATTER PHYSICS
local.identifier.ariespublicationU3488905xPUB4400
local.type.statusPublished Version
local.contributor.affiliationHyde, Stephen, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationRamsden, Stuart, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationRobins, Vanessa, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage319
local.bibliographicCitation.lastpage337
local.identifier.doi10.1107/S205327331400549X
dc.date.updated2015-12-11T08:56:11Z
local.identifier.scopusID2-s2.0-84905456552
local.identifier.thomsonID000341686000003
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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