2D hyperbolic groups induce three-periodic Euclidean reticulations

V. Robins*, S. J. Ramsden, S. T. Hyde

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    29 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)365-375
    Number of pages11
    JournalEuropean Physical Journal B
    Issue number3
    Publication statusPublished - 2004


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