This is a 2-dimensional family of genus 5 triply periodic minimal surfaces with the symmetries of a rectangular box. The divisor of the square of the Gauss map is given below.
The parameters need to satisfy b+c=a+d+1/2. There are at least three different types of limits. Two of them are nodal planes and can be used to prove the existence of these surfaces:
The third limit consists of doubly periodic Wei surfaces, stitched together with catenoidal necks.
Resources
PoVRay Sources
Minimal Surfaces 