Triply periodic minimal surface

In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in that is invariant under a rank-3 lattice of translations.

These surfaces have the symmetries of a crystallographic group. Numerous examples are known with cubic, tetragonal, rhombohedral, and orthorhombic symmetries. Monoclinic and triclinic examples are certain to exist, but have proven hard to parametrise.

TPMS are of relevance in natural science. TPMS have been observed as biological membranes, as block copolymers, equipotential surfaces in crystals etc. They have also been of interest in architecture, design and art.

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