Klein Bottle Mesh Vase

44WireFrameBottleVase_fixed.stl

Single Body Klein Bottle

One Solid Body Klein.3MF

Klein Bottle Diamond Lattice

Klein Bottle - Diamond Lattice.stl

Chain Link Klein Bottle

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.


klein bottle

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Single Body Klein Bottle

Klein Bottle Diamond Lattice

Chain Link Klein Bottle