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At sixes and sevens, and eights, and nines: schwarzites p 3, p = 7, 8, 9

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All is uneven. And everything is left at six and seven.

W. Shakespeare [1]

The Answer to the Great Question…. of Life, the Universe and Everything Is… Forty-two (6 × 7).

C. Adams [2]

Abstract

Examples are given of vertex and/or face-transitive p 3 (p = 7, 8, 9) tilings of periodic minimal surfaces. Infinite families of tilings, including aperiodic structures, are readily derived from some of these. They are of particular interest for theoretical studies of potential carbon allotropes.

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Acknowledgments

Help for that from Vladislav Blatov and Davide Proserpio is gratefully acknowledged. Work by MOK is supported by the IS National Science Foundation Grant DMR 1104798.

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Authors and Affiliations

  1. Applied Mathematics Department, School of Physical Sciences, Australian National University, Canberra, ACT, 0200, Australia

    Stephen T. Hyde

  2. School of Molecular Sciences, Arizona State University, Tempe, AZ, 85287, USA

    Michael O’Keeffe

Authors
  1. Stephen T. Hyde
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  2. Michael O’Keeffe
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Correspondence to Michael O’Keeffe.

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Hyde, S.T., O’Keeffe, M. At sixes and sevens, and eights, and nines: schwarzites p 3, p = 7, 8, 9. Struct Chem 28, 113–121 (2017). https://doi.org/10.1007/s11224-016-0782-1

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  • DOI: https://doi.org/10.1007/s11224-016-0782-1

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