In geometry, flexagons are flat models made from folded strips of paper that can be folded, or flexed, to reveal a number of hidden faces. They are amusing toys but have also caught the interest of mathematicians.

Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A flexagon whose hexagonal faces are each divided into twelve right triangles as opposed to six equilateral triangles, and which can consequently flex into nonhexagonal shapes, has recently been christened a dodecaflexagon (^*). A prefix can be added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a flexagon with a total of six faces is called a hexahexaflexagon.

The discovery of the first flexagon, a trihexaflexagon, is credited to the British student Arthur H. Stone who was studying at Princeton University in the USA in 1939, allegedly while he was playing with the strips he had cut off his A4 paper to convert it to letter size. Stone's colleagues Bryant Tuckerman, Richard P. Feynman and John W. Tukey became interested in the idea. Tuckerman worked out a topological method, called the Tuckerman traverse, for revealing all the faces of a flexagon. Tukey and Feynman developed a complete mathematical theory that has not been published.

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