Trading spaces: Building three-dimensional nets from two-dimensional tilings
-
Altmetric Citations
Castle, Toen; Evans, Myfanwy; Hyde, Stephen; Ramsden, Stuart; Robins, Vanessa
Description
We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns,...[Show more]
dc.contributor.author | Castle, Toen | |
---|---|---|
dc.contributor.author | Evans, Myfanwy | |
dc.contributor.author | Hyde, Stephen | |
dc.contributor.author | Ramsden, Stuart | |
dc.contributor.author | Robins, Vanessa | |
dc.date.accessioned | 2015-12-10T23:18:50Z | |
dc.identifier.issn | 2042-8901 | |
dc.identifier.uri | http://hdl.handle.net/1885/65803 | |
dc.description.abstract | We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions. | |
dc.publisher | Royal Society Publishing | |
dc.source | Interface Focus | |
dc.subject | Keywords: Symmetry; Three-dimensional tiling; Two-dimensional nets | |
dc.title | Trading spaces: Building three-dimensional nets from two-dimensional tilings | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 2 | |
dc.date.issued | 2012 | |
local.identifier.absfor | 020406 - Surfaces and Structural Properties of Condensed Matter | |
local.identifier.absfor | 010299 - Applied Mathematics not elsewhere classified | |
local.identifier.ariespublication | f5625xPUB1163 | |
local.type.status | Published Version | |
local.contributor.affiliation | Castle, Toen, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Evans, Myfanwy, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Hyde, Stephen, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Ramsden, Stuart, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Robins, Vanessa, College of Physical and Mathematical Sciences, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 5 | |
local.bibliographicCitation.startpage | 555 | |
local.bibliographicCitation.lastpage | 566 | |
local.identifier.doi | 10.1098/rsfs.2011.0115 | |
dc.date.updated | 2016-02-24T08:38:59Z | |
local.identifier.scopusID | 2-s2.0-84865354286 | |
local.identifier.thomsonID | 000308239700004 | |
Collections | ANU Research Publications |
Download
File | Description | Size | Format | Image |
---|---|---|---|---|
01_Castle_Trading_spaces:_Building_2012.pdf | 2.94 MB | Adobe PDF | Request a copy |
Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.
Updated: 17 November 2022/ Responsible Officer: University Librarian/ Page Contact: Library Systems & Web Coordinator