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

Ramsden, Stuart; Robins, Vanessa; Hyde, Stephen

Description

We 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...[Show more]

CollectionsANU Research Publications
Date published: 2009
Type: Journal article
URI: http://hdl.handle.net/1885/35857
Source: Acta Crystallographica Section A: Foundations of Crystallography
DOI: 10.1107/S0108767308040592

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