Multiple KLEIN BOTTLES inside/outside eachother

For those of you unfamiliar with a Klein Bottle, it has the special property in that it's surface (both interior and exterior) are the same. In our universe of three dimensions, we can only come up with an approximation of a true Klein bottle.

Taking it a step further, Alan Bennett of Bedford, UK created three Klein bottles set inside eachother as shown above.

Here is an animation of how a Klein bottle is formed:

Links:
Glass Triple Klein Bottle (Science Museum)
Klein Bottle Wiki
Imaging Maths - Inside the Klein Bottle