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Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples

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dc.contributor.authorRamsden, Stuart
dc.contributor.authorRobins, Vanessa
dc.contributor.authorHyde, Stephen
dc.date.accessioned2015-12-08T22:38:33Z
dc.date.issued2009
dc.date.updated2016-02-24T10:54:56Z
dc.description.abstractWe present a method for geometric construction of periodic three-dimensional Euclidean nets by projecting two-dimensional hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMSs). Our techniques extend the combinatorial tiling theory of Dress, Huson & Delgado-Friedrichs to enumerate simple reticulations of these TPMSs. We include a taxonomy of all networks arising from kaleidoscopic hyperbolic tilings with up to two distinct tile types (and their duals, with two distinct vertices), mapped to three related TPMSs, namely Schwarz's primitive (P) and diamond (D) surfaces, and Schoen's gyroid (G).
dc.identifier.issn0108-7673
dc.identifier.urihttp://hdl.handle.net/1885/35857
dc.publisherMunksgaard International Publishers
dc.sourceActa Crystallographica Section A: Foundations of Crystallography
dc.subjectKeywords: Kaleidoscopic hyperbolic tilings; Three-dimensional Euclidean nets; Triply periodic minimal surfaces; Two-dimensional hyperbolic tilings
dc.titleThree-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples
dc.typeJournal article
local.bibliographicCitation.lastpage108
local.bibliographicCitation.startpage81
local.contributor.affiliationRamsden, Stuart, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationRobins, Vanessa, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationHyde, Stephen, College of Physical and Mathematical Sciences, ANU
local.contributor.authoruidRamsden, Stuart, u9311731
local.contributor.authoruidRobins, Vanessa, u9213671
local.contributor.authoruidHyde, Stephen, u8604415
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor020406 - Surfaces and Structural Properties of Condensed Matter
local.identifier.absfor010299 - Applied Mathematics not elsewhere classified
local.identifier.ariespublicationu4326120xPUB129
local.identifier.citationvolumeA65
local.identifier.doi10.1107/S0108767308040592
local.identifier.scopusID2-s2.0-60749132004
local.identifier.thomsonID000263517500001
local.type.statusPublished Version

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