[xznzjieg] Minimum number of fixed points on the hairy ball

The Hairy Ball Theorem states that there must be at least one pole.  Mapping a sphere onto a rotation of itself yields two poles, and one might conjecture there must be at least two.  This is false: it can be done with just one, as illustrated on the current Wikipedia page.

Very roughly, take the two poles and mash them together, creating a single-point dipole.