stereotypical topologist's family puzzle
grabcad
Klein bottle immersed into 3d space splits into two Möbius strips. Möbius strip cut down the middle lengthwise becomes a double twisted strip. Möbius strip cut off the middle lengthwise splits into a smaller Möbius strip and linked double twisted strip. A bust of local politician moves along the railing in and out of the bottle to demonstrate onesidedness, flip-flopping and disorientability (next version).
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