Klein bottle

A non-intersecting 4-D parametrization can be modeled after that of the flat torus:

The parametrization of the 3-dimensional immersion of the bottle itself is much more complicated.

The traditional Klein bottle immersion is achiral. The figure-8 immersion is chiral. (The pinched torus immersion above is not regular, as it has pinch points, so it is not relevant to this section.)