Hyperbolic crystallography of two-periodic surfaces and associated structures
dc.contributor.author | Pedersen, Martin | |
dc.contributor.author | Hyde, Stephen | |
dc.date.accessioned | 2020-12-20T20:56:57Z | |
dc.date.available | 2020-12-20T20:56:57Z | |
dc.date.issued | 2017 | |
dc.date.updated | 2020-11-23T10:38:49Z | |
dc.description.abstract | This 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.mimetype | application/pdf | en_AU |
dc.identifier.issn | 2053-2733 | |
dc.identifier.uri | http://hdl.handle.net/1885/218109 | |
dc.language.iso | en_AU | en_AU |
dc.publisher | Wiley-Blackwell Publishing Ltd | |
dc.source | Acta Crystallographica. Section A | |
dc.title | Hyperbolic crystallography of two-periodic surfaces and associated structures | |
dc.type | Journal article | |
local.bibliographicCitation.issue | 2 | |
local.contributor.affiliation | Pedersen, Martin, College of Science, ANU | |
local.contributor.affiliation | Hyde, Stephen, College of Science, ANU | |
local.contributor.authoremail | u8604415@anu.edu.au | |
local.contributor.authoruid | Pedersen, Martin, u1003767 | |
local.contributor.authoruid | Hyde, Stephen, u8604415 | |
local.description.notes | Imported from ARIES | |
local.identifier.absfor | 010102 - Algebraic and Differential Geometry | |
local.identifier.absfor | 040306 - Mineralogy and Crystallography | |
local.identifier.absseo | 970101 - Expanding Knowledge in the Mathematical Sciences | |
local.identifier.ariespublication | a383154xPUB5314 | |
local.identifier.citationvolume | 73 | |
local.identifier.doi | 10.1107/S2053273316019112 | |
local.identifier.scopusID | 2-s2.0-85014351462 | |
local.identifier.thomsonID | 000396046500006 | |
local.identifier.uidSubmittedBy | a383154 | |
local.type.status | Published Version |