This translation invariant surface was discovered in 2009 by Márcio Fabio da Silva and Valério Ramos Batista. It features 8 annular ends and has genus 2.

The construction assumes reflectional symmetries at the coordinate planes, making it a 2-dimensional family. Thus it resembles in many ways another 8-ended genus 2 Scherk surface. The differences become apparent close to their respective limits. In one extreme case, one obtains Wohlgemuth surfaces of genus 2:

In a second extreme case, two halves of the surface separate and converge to 6-ended Scherk surfaces with one pair of annular ends becoming parallel:

The two pieces are then stitched together using catenoidal necks. The current existence proof is long and tedious and requires to solve a 3-dimensional period problem. It would be interesting to incorporate this surface into a triply periodic version. It would also be interesting to show that this surface cannot be deformed into the other genus 2, 8-ended surface.

Resources

M.F. da Silva, V. Ramos Batista: Scherk Saddle Towers of Genus Two in R³

Mathematica Notebook

PoVRay Sources