The deformation family of this surface imperceptibly moves the small handle up and down. One of the limits is an exotic Karcher-Scherk surface whose existence has not been established. 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 the exotic/experimental Karcher-Scherk surface of genus 3 joined end-to-end with a genus 0 Scherk surface, the right uses two genus 0 and one genus 1 Karcher-Scherk surface.

Resources

Mathematica Notebook

PoVRay Sources