Try me.
Okay, kiddo.
The Klein bottle is not four dimensional. If you don't believe me look at its Wikipedia page, where you can clearly see it constructed in 3d. If it was 4-d, there would be no way to construct it in 3d without loosing some amount of information.
The Klein bottle in
reality is 4th dimensional, therefore does not exist.
The
representations you see on the OP and throughout this thread are simply that, fake representations. The one in the OP is simple glass work. The other pictures posted are simple models made in a 3D Modeling program.
The real, mathematical Klein bottle
does not and cannot exist in our 3-dimensional plane. It is called math. Learn it.
Furthermore, while it is true that it technically has no area (as it intersects itself), that does not mean that it could not contain liquid or that mathematically it shouldn't be able to hold anything. This is basic physics.
You must be failing math or your teacher is a bloody moron.
The 4th dimension is said to completely obliterate all current laws of physics because our physics are meant for the 3rd dimension, not the 4th. In reality and in math, a real, 4-dimensional Klein bottle defies human physics because it is imperceptible.
Go back to school.