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2D Hyperbolic Groups Induce Three-periodic Euclidean Reticulations

Robins, Vanessa; Ramsden, Stuart; Hyde, Stephen


Many crystalline networks can be viewed as decorations of triply periodic minimal surfaces. Such surfaces are covered by the hyperbolic plane in the same way that the Euclidean plane covers a cylinder. Thus, a symmetric hyperbolic network can be wrapped onto an appropriate minimal surface to obtain a 3d periodic net. This requires symmetries of the hyperbolic net to match the symmetries of the minimal surface. We describe a systematic algorithm to find all the hyperbolic symmetries that are...[Show more]

CollectionsANU Research Publications
Date published: 2004
Type: Journal article
Source: European Physical Journal B


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