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The Klein Bottle The Klein bottle is another unorientable surface. It can be constructed by gluing together the two ends of a cylindrical tube with a twist. Unfortunately this can't be realized physically in 3-dimensional space. The best we can do is to pass one of the ends into the interior of the tube at the other end (while simultaneously inflating the tube at this second end) before gluing ...
www.math.ohio-state.edu/~fiedorow/math655/Klein2.html
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