# Periodic minimal surfaces

@article{Mackay1985PeriodicMS, title={Periodic minimal surfaces}, author={Alan Lindsay Mackay}, journal={Nature}, year={1985}, volume={314}, pages={604-606} }

A minimal surface is one for which, like a soap film with the same pressure on each side, the mean curvature is zero and, thus, is one where the two principal curvatures are equal and opposite at every point. For every closed circuit in the surface, the area is a minimum. Schwarz1 and Neovius2 showed that elements of such surfaces could be put together to give surfaces periodic in three dimensions. These periodic minimal surfaces are geometrical invariants, as are the regular polyhedra, but the…

## 94 Citations

Periodic Surfaces of Prescribed Mean Curvature

- Mathematics
- 1987

While there are eighteen triply periodic minimal surfaces that reportedly are free of self-intersections, to date there is no known example of a triply periodic surface of constant, nonzero mean…

Films of Amphiphiles and Minimal Surfaces

- Mathematics
- 1992

A film of amphiphiles is made of two identical facing interfaces and its middle surface is a surface of symmetry. This symmetry leads the structures built by the film to be considered as…

Micelles and Foams: 2-D Manifolds Arising from Local Interactions

- Mathematics
- 1993

Surfaces as 2-D manifolds play an important role in the description of structures, from inorganic materials to biological systems. These surfaces which can be planar, spherical or hyperbolic…

Triply periodic surfaces and multiply continuous structures from the Landau model of microemulsions.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

It is observed that multiply continuous structures are most easily generated close to the water-oil coexistence region, and the geometrical characteristics of these phases, such as genus per unit cell, surface area per unit volume, and volume fraction occupied by oil or water, are studied.

Scattering on triply periodic minimal surfaces—the effect of the topology, Debye-Waller, and molecular form factors

- Mathematics
- 2000

We compute scattering patterns for four triply periodic surfaces (TPS). Three minimal—Schwarz P (Im3m), Schwarz D—diamond (Pn3m), Schoen G—gyroid (Ia3d), and one nodal S1 (Ia3d). Simple…

Topological Versus Physical and Chemical Properties of Negatively Curved Carbon Surfaces

- Physics
- 2013

Some relevant physical and chemical properties of negatively curved carbon surfaces like sp 2-bonded schwarzites can be predicted or accounted for on the basis of purely topological arguments. The…

Periodic systems of frustrated fluid films and « bicontinuous » cubic structures in liquid crystals

- Materials Science
- 1987

We consider periodic organizations of two fluid media separated by interfaces in which interactions between the two media, normal to the interfaces, maintain constant distances between interfaces and…

Minimal surfaces with self-intersections along straight lines. I. Derivation and properties.

- MathematicsActa crystallographica. Section A, Foundations of crystallography
- 1999

A special kind of three-periodic minimal surface has been studied, namely surfaces that are generated from disc-like-spanned skew polygons and that intersect themselves exclusively along straight…

Infinite Periodic Minimal Surfaces: A Model for Blue Phases

- Mathematics
- 1990

Abstract The local constraint of double twist cannot lead to long range order in our physical space ℝ. Cubic blue phases can be interpreted as an array of disclination lines. The symmetry 1432, P4232…

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