This is an example that exhibits higher genus Callahan-Hoffman-Meeks surfaces as a limit. The divisor of the squared Gauss map is below.

Below are 8 copies of a translational fundamental piece near the two limits: The left limit consists of Callahan-Hoffman-Meeks surfaces with added handles, the right uses genus 0/1 Karcher-Scherk surfaces with catenoidal stitches.

Resources

Mathematica Notebook

PoVRay Sources