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

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 \(\mathbb{E}^3\).