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Trading spaces: Building three-dimensional nets from two-dimensional tilings

Castle, Toen; Evans, Myfanwy; Hyde, Stephen; Ramsden, Stuart; Robins, Vanessa


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]

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Interface Focus
DOI: 10.1098/rsfs.2011.0115


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