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Symmetry Groups and Reticulations of the Hexagonal H Surface

Robins, Vanessa; Ramsden, Stuart; Hyde, Stephen


We describe a systematic approach to generate nets that arise from decorations of 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. Here, we tabulate all such symmetry groups that are compatible with...[Show more]

CollectionsANU Research Publications
Date published: 2004
Type: Journal article
Source: Physica A: Statistical mechanics and its applications
DOI: 10.1016/j.physa.2004.03.053


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