Topological Glue
Looking at the two squares below : if you glue the top edge to the bottom such as the arrows stay oriented the same, you will have constructed a cylinder and a Möbius strip respectively.
What will you construct now if we glue the right edge to the bottom such as the arrows stay oriented the same ?
Hint : You are allow to make a cut but you have to glue it back with the same orientation.
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1 solution
The trick is to make a diagonal cut, twist the left side in order to glue the initial arrows together, and then we have the Möbius strip configuration back :