2D hyperbolic groups induce three-periodic Euclidean reticulations

V. Robins (), S. Ramsden and S. Hyde

The European Physical Journal B: Condensed Matter and Complex Systems, 2004, vol. 39, issue 3, 365-375

Abstract: 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 commensurate with a given minimal surface, and the generation of simple 3d nets from these symmetry groups. Copyright Springer-Verlag Berlin/Heidelberg 2004

Date: 2004
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DOI: 10.1140/epjb/e2004-00202-2

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