Does the Klein bottle exist?

Such an object is a contradiction, and cannot exist any more than a 4 sided triangle.

Not sure if I'm missing an inside joke or something but you can make one if you're a skilled glassblower...  the shape isn't impossible, just stop seeing the intersection as non-interfering and it makes rational sense.  The outside is the outside and the inside is the inside because the surfaces intersect.  The surface does not truly continue in a rational sense