A triply periodic minimal surface is a minimal surface in three-dimensional Euclidean space which is
invariant under translations by three linearly independent
vectors. These vectors generate a rank-3 lattice 
,
and the surface descends to a compact minimal surface
in the flat three-dimensional torus 
.
Classical examples include Schwarz's P and D surfaces and the gyroid. Their periodic complements commonly divide space into two interwoven labyrinths, and their geometry is studied through the topology and conformal structure of the compact quotient surface.
