The Schwarz D surface is an embedded surface that is a triply periodic minimal surface and separates three-dimensional Euclidean space into two congruent, interwoven labyrinths whose skeletons have the structure of the diamond crystal network. Each network junction has four neighbors at the vertices of a tetrahedron. The letter D stands for diamond (Schoen 1970, pp. 1-6, 37-39).
The translations that preserve each labyrinth form a face-centered cubic lattice. The compact surface obtained by identifying points equivalent under these translations has genus 3 (Schoen 1970, p. 6). The surface has translations that interchange its two labyrinths, so a translational unit cell for either labyrinth is larger than a translational unit cell for the surface (Brakke).
The Schwarz D surface is locally isometric to the Schwarz P surface and the gyroid, although their labyrinths have different structures (Brakke).
