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 $\mathrm{Ia}\overline{3}d$ 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.

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