It can be constructed by gluing the opposite edges of a rectangle together with no twists.
This shape is a a Dupin cyclide of characteristic one comma one. Like the Klein Bottle and cylinder, it has an Euler characteristic of zero, and the ordinary one has a genus of one. According to the Heawood conjecture, it can be colored with seven colors. It can be described as the (*) Cartesian product of two circles. It can be constructed by gluing the opposite edges of a rectangle together with no twists. For 10 points, name this donut-shaped mathematical surface.
This shape is a a Dupin cyclide of characteristic one comma one.
torus