Hexaflexagons were invented by a Princeton University student in 1939, but Flexagons were introduced to the general public by the recreational mathematician Martin Gardner in 1956 in the first Mathematical Games column which he wrote for Scientific American magazine. In 1974, the magician Doug Henning included a construct-your-own hexaflexagon with the original cast recording of his Broadway show The Magic Show.
Hexaflexagons are folded figures that have more "sides" than the two you can see. This one has six different sides as you flex through them, but three of those are very hard to find. Print out this figure (right click on strip, choose "print") and then carefully cut it out. Follow the instructions on how to fold it (you can use tape instead of glue). Get help from the link below, if needed. Have Fun!
If you can use some help or hints, try Wikipedia.