This model uses chain link latticing to represent a three-dimensional approximation of the four-dimensional “Klein Bottle.”

See here for video: https://youtu.be/AWJ-R3GBT80

The concept of a Klein bottle was first described in 1882 by the German mathematician Felix Klein. It is a closed non-orientable surface that has no inside or outside. It is similar to the Möbius strip, but unlike the Möbius strip it has no boundaries and cannot physically exist in three-dimensional space.

In this three-dimensional representation, the surface intersects with itself, but in four-dimensional space the self-intersection can be eliminated. Unfortunately, I don’t have a 4D printer yet.

Modelling this intriguing shape in chain link latticing allows for visualization of the whole surface.