My undergraduate student and I are working through chapter 2 of the book Complex Analysis Topics for Undergraduates and Beginning Researchers: an Exploration with Unsolved Problems, (http://www.jimrolf.com/explorationsInComplexVariables/explorationsComplexVariables6.7.11.pdf).
They have been working to find a parametrization for the octoid, which is a minimal surface in $\mathbb{R}^3$ with six catenoidal ends that stick out along the positive and negative x, y, and z axes. In particular, we would like to find the Gauss map and height differential for this surface.
We have been trying everything we could think of, but with no luck so far. My student is going to move on to another project, but I am dying of curiosity. Does anyone know of a "nice" parametrization, or Weierstrauss representation, for this surface?
I've searched the web and found many seemingly promising results, but the most I could find is a proof that this and many related minimal surfaces exist.
Thank you in advance.