Diabolical Möbius strip variant

Feynman had a punchline about physics:x=maths:y and we think it’s only fair that we should be allowed, too, to do some math with our hands.

Make these out of paper and cut them along the dotted line. 

What happens? Why?


Credits and source attribution
James Tanton, Solve This: Math Activities for Students and Clubs, page 19
(G’day beautiful Australia and Adelaide! South Australia is home to the only palindrome toponym I ever visited. What about you readers?)

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