There are some other fun videos that demonstrate why exactly these work, and some with even more than three sides! Check them out:
https://www.youtube.com/watch?v=VIVIegSt81k
My math teacher also decided to have fun with this (as if these are not already fun) by showing us these funnier videos on hexaflexagons (warning, video four may cause hunger):
https://www.youtube.com/watch?v=GTwrVAbV56o