https://doi.org/10.1140/epjb/e2005-00377-x
A note on the two symmetry-preserving covering maps of the gyroid minimal surface
Department of Applied Mathematics, Research School of Physical Sciences, The Australian National University, Canberra ACT 0200, Australia
Corresponding author: a vanessa.robins@anu.edu.au
Received:
21
June
2005
Published online:
9
December
2005
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 
is chiral, the projection of this pattern via the two covering maps gives rise to distinct structures in 
.
PACS: 61.50.Ah – Theory of crystal structure, crystal symmetry; calculations and modeling / 89.75.Hc – Networks and genealogical trees / 02.20.-a – Group Theory / 02.40.-k – Geometry, differential geometry, and topology
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
