Question: What was created in 1939 that piqued the interest of such brilliant and diverse minds as Richard Feynman and Martin Gardner, but was simple enough to build that it became a fad for schoolchildren?
The Hexahexaflexagon is the best of the Flexagons. There are numerous sites with history and information. As far as building your own - check out this site or this site. If you have kids, make it a family project. If you don't have kids, then you have plenty of time on your hands to make one for yourself.
Interesting and cool - you won't be disappointed. Top Men would not lie to you.