The orthorhombic deformation of Hermann Amandus Schwarz Diamond surface consists of the conjugate surfaces of the oP deformation and solves the Plateau problem for a hexagon whose sides follow the edges of a box:
Below are twice a fundamental piece (the lattice is base-centered orthorhombic) and 8 copies of that.
This deformation comes with two parameters (the dimensions of the box modulo scaling). In the torus quotient under the order 2 rotational symmetry, the square of the Gauss map has the divisor below. Here the parameters are the torus parameter τ and the location a of the points with vertical normal.
In turn, the original Diamond surface is a special case of this family.