Here are photos of some of my students' hexaflexagons and how to flex them:
I used hexaflexagons in my geometry and calculus classes from 1986 to 2006, but my favorite hexaflexagon came from a former student in 2002. Theresa had graduated frm Handley in 1997 and graduated from the University of Virginia in 2001 and then went on to serve in the Peace Corps in North Farawa on the island of Kiributi. She sent me a letter on the six sides of the hexaflexagon! Below is her hexaflexagon from half way around the world!
When you flex the hexafleagon, the same side can give two different pictures. Theresa was kind enough to number the sides to help me with the correct orientation of her letter. She put the numbers all together in the center of the hexaflexagon. You can see this in the next two photos -- the correct orientation is in the first.
