I think such a surface would likely resemble a monkey saddle, since it seems to have the same symmetry. It's not clear to me that there is a unique minimal surface, or perhaps two congruent ones neither of which include the centroid. But there is software developed by Ken Brakke called the Surface Evolver that is designed to calculate (and draw, with an external drawing program) minimal surfaces with a given boundary, and related optimization problems: http://facstaff.susqu.edu/brakke/evolver/evolver.html <http://facstaff.susqu.edu/brakke/evolver/evolver.html>. —Dan
On Jan 4, 2016, at 11:04 AM, James Propp <jamespropp@gmail.com> wrote:
Do any of you know of any pictures (hand-drawn or computer-generated) of the saddle-shaped surface you get when you make a non-planar hexagonal frame consisting of all the edges of a cube that avoid two antipodal vertices an dip it in a soap film solution?
This is not to be confused with the surface you get when you dip a non-planar octagonal frame consisting of the edges in a Hamiltonian cycle on the cube.
I spent about five minutes searching images.google.com and didn't find what I'm looking for, and would appreciate help from any of you who may know about where such things can be found!
Thanks,