I have been making math-based sculptures using a 3D printer and other techniques. For a few months I have been working with the approximate gyroid surface in Cartesian coordinates defined by
Cos(y) Sin(x)+ Cos(z) Sin(y) + Cos(x])Sin(z) = 0 for real 0 <= x, y, z <= 2 pi.
This is periodic, of course, in each of the three coordinates, but I am only considering one period of each as a connected surface of genus... I think genus 3. At this point I need a little bit of help understanding the symmetry properties of the algebraic expression and the geometric figure. I would estimate this at about 1-3 hours assuming the teacher is familiar with 3D symmetry operations and defining the appropriate group. I am not conversant with that.