Triply Periodic Minimal Surfaces

Zero mean-curvature surfaces that tile 3D space: the Schwarz P surface (cos x + cos y + cos z = 0) and Schoen's Gyroid (sin x cos y + sin y cos z + sin z cos x = 0).

Minimal surfaces satisfy the Euler-Lagrange equation H=0 (mean curvature vanishes). TPMS found in block copolymer self-assembly, butterfly wing nanostructures, and bone trabecular architecture. Visualization: ray-marched implicit surface F(x,y,z)=iso rendered with normal-shaded lighting.