Hyperbolic crystallography of two-periodic surfaces and associated structures

dc.contributor.authorPedersen, Martin
dc.contributor.authorHyde, Stephen
dc.date.accessioned2020-12-20T20:56:57Z
dc.date.available2020-12-20T20:56:57Z
dc.date.issued2017
dc.date.updated2020-11-23T10:38:49Z
dc.description.abstractThis paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group-subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol and a surface decoration.The intrinsic, hyperbolic crystallography of the two-periodic, genus-two HCB and SQL surfaces is presented. All discrete groups containing the translations of the Euclidean embeddings of these surfaces are derived and examples of applications are given
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn2053-2733
dc.identifier.urihttp://hdl.handle.net/1885/218109
dc.language.isoen_AUen_AU
dc.publisherWiley-Blackwell Publishing Ltd
dc.sourceActa Crystallographica. Section A
dc.titleHyperbolic crystallography of two-periodic surfaces and associated structures
dc.typeJournal article
local.bibliographicCitation.issue2
local.contributor.affiliationPedersen, Martin, College of Science, ANU
local.contributor.affiliationHyde, Stephen, College of Science, ANU
local.contributor.authoremailu8604415@anu.edu.au
local.contributor.authoruidPedersen, Martin, u1003767
local.contributor.authoruidHyde, Stephen, u8604415
local.description.notesImported from ARIES
local.identifier.absfor010102 - Algebraic and Differential Geometry
local.identifier.absfor040306 - Mineralogy and Crystallography
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
local.identifier.ariespublicationa383154xPUB5314
local.identifier.citationvolume73
local.identifier.doi10.1107/S2053273316019112
local.identifier.scopusID2-s2.0-85014351462
local.identifier.thomsonID000396046500006
local.identifier.uidSubmittedBya383154
local.type.statusPublished Version

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