This is a surface with interesting limits. The divisor of the squared Gauss map is below.

Below are 8 copies of a translational fundamental piece near the two limits: Two doubly periodic Karcher-Scherk surfaces of genus 0 and 2 on the left (with catenoidal stitches), and horizontal planes joined by Costa and Catenoidal nodes.

This examples indicates that Costa and Catenoid nodes can occur simultaneously, at least between different planes.


Mathematica Notebook

PoVRay Sources