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Published on May 28, 2013
An investigation into how triply-periodic minimal surfaces are defined, derived, and classified. Includes description of examples known in 1972. Plateau's problem. Fundamental concepts of the differential geometry of minimal surfaces, including the Schwarz reflection principle; Euler characteristic; mean curvature; Gaussian curvature; Gauss map of a surface by parallel normals onto the Riemann sphere; associate and adjoint surfaces; skeletal graphs; complementary minimal surfaces; the classical Schwarz surfaces and the gyroid.