Symmetry groups and reticulations of the hexagonal H surface

Vanessa Robins, S.J. Ramsden and Stephen T. Hyde

Physica A: Statistical Mechanics and its Applications, 2004, vol. 339, issue 1, 173-180

Abstract: 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 the H minimal surface.

Keywords: Hyperbolic tilings; Minimal surfaces; Networks; Frameworks; Reticular chemistry; Symmetry groups (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:339:y:2004:i:1:p:173-180

DOI: 10.1016/j.physa.2004.03.053

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