Parametrization of triply periodic minimal surfaces. II. Regular class solutions

A derivation is given of the set of triply periodic minimal surfaces of monoclinic symmetry and higher that fall within the regular class (including those containing self-intersections). The Gauss maps, Weierstrass parametrizations and asymmetric units of each surface are included. Triclinic relatives of monoclinic surfaces are also discussed. Some minimal surfaces that lack translational order but exhibit orientational symmetry also naturally appear within this derivation.