A flexagon is a hexagon, which you can make from a strip of triangles. The objective is to open the flexagon in the middle and have a previously hidden face appear.
Arthur Stone, an English graduate student, was in the practice of doodling with the strips of paper that he cut from around the edges of his notebook paper. American paper was too large for his English binder. One of the constructions arising from this happy misfortune attracted his attention in particular. A committee of graduate students formed to solve the mystery of the "flexible hexagon", or, as it soon became known, the "flexagon."
The members of this group-- Richard P. Feynman, Bryant Tuckerman, John W. Tukey, and Arthur H. Stone, had laid the groundwork for all consequent study, through developing their yet unpublished theory, by the early 1940's. When the group disbanded, the flexagon was left, nearly forgotten, for ten years. Then, toward the beginning of the fifties, it received slight publicity with several very brief articles in mathematics magazines.