Klein bottle immersed in $\mathbb{R}^3$, a closed non-orientable surface with a circle of self-intersection
The Klein bottle is a closed non-orientable surface that cannot be embedded in R3 without self-intersection. This visualization uses the standard immersion that passes the neck of the bottle through its own side, creating a circle of self-intersection. The Klein bottle can be constructed by gluing two Mobius bands along their boundaries, and it has Euler characteristic zero.
Controls: Click and drag to orbit, scroll to zoom.
