This surface has integrable geodesic flow. That means that if you know where you stand on the surface and for how long you go ahead as straight as possible on a curved surface, you can use a closed formula to calculate exactly where you will arrive.
Thanks to Prof. Thomas Waters for teaching me how to construct these surfaces.
This shape is a (7, 2)-torus knot.
Also available: (5, 3) (5, 4) (6, 5) (7, 5)