It's an established mathematical term for these things. Of course, mathematical terms tend to be "made up" at some point, but I don't think that's a useful distinction.
It's going to blow your mind when you realize all words are made up. Even more so when you find out that definitions change and new words are invented every year.
I made some tetra-tetra-flexagons for my wedding, and in the process made an ImageMagick script to take four images and turn them into two, one for each side of the sheet of paper.
I still have a 24-faced hexaflexagon I made in 1975, using onionskin paper and an HP plotter. (Thinness and accuracy are critical for high-order flexagons.)
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[ 3.1 ms ] story [ 46.6 ms ] threadThe wikipedia page [1] on the things is a good introduction too.
[1] https://en.wikipedia.org/wiki/Flexagon
http://www.marriedtothesea.com/030807/dictionary.gif
https://news.ycombinator.com/newsguidelines.html
https://www.timpark.org/making-a-tetratetraflexagon/ (unfortunately some of the external links are broken, I should do some editing)
http://underlandia.com/index.php/2017/07/17/things-of-scienc...
[0] https://www.youtube.com/watch?v=VIVIegSt81k