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.


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