Skip to main content
SpringerLink
Log in

A note on the two symmetry-preserving covering maps of the gyroid minimal surface

  • Mathematical Physics
  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

Our study of the gyroid minimal surface has revealed that there are two distinct covering maps from the hyperbolic plane onto the surface that respect its intrinsic symmetries. We show that if a decoration of \(\mathbb{H}^2\) is chiral, the projection of this pattern via the two covering maps gives rise to distinct structures in \(\mathbb{E}^3\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • V. Robins, S.J. Ramsden, S.T. Hyde, Eur. Phys. J. B 39, 365 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  • V. Robins, S.J. Ramsden, S.T. Hyde, Physica A 339, 173 (2004)

    Article  ADS  ISI  MathSciNet  Google Scholar 

  • S.T. Hyde, A.-K. Larsson, T. DiMatteo, S.J. Ramsden, V. Robins, Australian J. Chem. 56, 981 (2003)

    Article  Google Scholar 

  • S.T. Hyde, S.J. Ramsden, Eur. Phys. J. B 31, 273 (2003)

    Article  ADS  Google Scholar 

  • S.T. Hyde, S.J. Ramsden, edited by D. Bonchev, D.H. Rouvray, Chemical Topology: Applications and Techniques, Chap. 2, p. 35 (Gordon and Breach Science, Amsterdam, 2000)

  • C. Oguey, J.-F. Sadoc, J. Phys. I 3, 839 (1993)

    Article  Google Scholar 

  • J.-F. Sadoc, J. Charvolin, Acta Cryst. A 45, 10 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • A. Fogden, S.T. Hyde, Eur. Phys. J. B 7, 91 (1999)

    Article  ADS  Google Scholar 

  • A. Fogden, M. Haeberlein, S. Lidin, J Phys. I France 3, 2371 (1993)

    Article  MathSciNet  Google Scholar 

  • M. O'Keeffe, The Materials Design and Discovery Group. The Reticular Chemistry Structure Resource, May 2005 online database available at http://okeeffe-ws1.la.asu.edu/RCSR/home.htm

  • X. Zou, T. Conradsson, M. Klingstedt, M.S. Dadachov, M. O'Keeffe, Nature 437, 716 (2005)

    Article  ADS  ISI  Google Scholar 

  • J.H. Conway, The orbifold notation for surface groups, in Groups, combinatorics, and geometry, LMS Lecture Notes 165 (Cambridge University Press, 1992), p. 438

  • J.H. Conway, D.H. Huson, Structural Chemistry 13, 247 (2002)

    Article  ISI  Google Scholar 

  • W. Fischer, Z. Krist. 138, 129 (1973)

    Article  Google Scholar 

  • W. Fischer, Z. Krist. 140, 50 (1974)

    Google Scholar 

  • M. O'Keeffe, B.G. Hyde, Crystal Structures I, Patterns and Symmetry (Mineralogical Society of America, Washington, DC, 1996)

Download references

Author information

Authors and Affiliations

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

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

Authors
  1. V. Robins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. J. Ramsden
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. T. Hyde
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Robins.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Robins, V., Ramsden, S. & Hyde, S. A note on the two symmetry-preserving covering maps of the gyroid minimal surface. Eur. Phys. J. B 48, 107–111 (2005). https://doi.org/10.1140/epjb/e2005-00377-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2005-00377-x

Keywords

Search

Navigation