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.

The images above are for a=.15 and τ=2i. Below is the surface for a=.15 and τ=0.5i.

In case that a=.25, we have additional diagonal horizontal lines and the surface lies in a box over a square. This 1-parameter tD subfamily is called the tetragonal D-family.

In turn, the original Diamond surface is a special case of this family.

Resources

Mathematica Notebook

PoVRay Sources