Surface of genus 2

This surface has equation $$ 4\sqrt{2}(x^2-y^2)z = (r^2-1)((r^2+1)^2-6z^2) $$ where $r=(x^2+y^2+z^2)^{1/2}$. It has genus two.

We can build a surface like this by pasting the sides of an octagon, following the pattern shown above on the right.