This object can be mapped using a variation of spherical coordinates consisting of the spherical angle theta and the poloidal angle phi.
An irrational line on this compact object will never self intersect and is a common topological counter example. This object can be mapped using a variation of spherical coordinates consisting of the spherical angle theta and the poloidal angle phi. A net for this object can be constructed by glueing parallel edges of a rectangle together, because this object is equal to the Cartesian product of two circles. A map on this object requires seven colors, and this object has genus one because it has a hole, making this shape topologically equivalent to a coffee cup. For 10 points, name this shape that looks like a donut.
An irrational line on this compact object will never self intersect and is a common topological counter example.
Ring {Torus} [prompt on "donut" before mentioned]