I haven't built a hexaflexagon in ages. Used to be big in my school in the late 70s, early 80s. When we taught a new person to fold one we used to tell the story of the guy who got his tie stuck in one ... The story came from two letters published in Scientific American in the May and March issues of 1957 in response to a Martin Gardner article on the flexagons.
Just went and bought a recording of the full show for a bank breaking $6... https://whataboutdick.com/