High Genus Periodic Gyroid Surfaces of Nonpositive Gaussian Curvature

In this paper we present a novel method for the generation of periodic embedded surfaces of nonpositive Gaussian curvature. The structures are related to the local minima of the scalar order parameter Landau-Ginzburg Hamiltonian for microemulsions. The method is used to generate six unknown surfaces of Ia3̄d symmetric (gyroid) of genus 21, 53, 69, 109, 141, and 157 per unit cell. All of them but that of genus 21 are most likely the minimal surfaces. The Schoen-Luzzati gyroid minimal surface of genus 5 (per unit cell) is also obtained.