This video is based on, and in honor of, Martin Gardner’s first Mathematical Games column from 1956, “Hexaflexagons,” which can be found here (pdf): http://maa.org/pubs/focus/Gardner_Hexaflexagons12_1956.pdf
October 21st is Martin Gardner’s birthday, which is why every October the recreational mathematics community celebrates his life and work. This year we’re having hexaflexagon parties. You can join in too: puzzles.com/hexaflexagon/
You can find more about hexaflexagons all over the internet. flexagons.net has a lot of patterns for different kinds of flexagons, or here’s the wikipedia page.