The Klein bottle was discovered in 1882 by Felix Klein and since then has joined the gallery of popular mathematical shapes.
The Klein bottle is a one-sided closed surface named after Klein. We note however this is not a continuous surface in 3-space as the surface cannot go through itself without a discontinuity.

Here is the result from the code above:

References

[Klein Bottle] (https://www.math.hmc.edu/funfacts/ffiles/30002.7.shtml)
[http://genedan.com/no-39-exploring-sage-as-an-alternative-to-mathematica/] (http://genedan.com/no-39-exploring-sage-as-an-alternative-to-mathematica/)
[Imaging maths - Inside the Klein bottle] (https://plus.maths.org/content/imaging-maths-inside-klein-bottle)
[Fun with surf3D function] (http://alstatr.blogspot.pt/2014/02/r-fun-with-surf3d-function.html)