Flexagons are an interesting diversion made from strips of paper. They fold flat, just showing two sides at a time. But you can "flex" it to bring new faces into view. The order the faces appear in as you flex isn't nearly as obvious as you might first expect.

There are many variations made with different polygons. The most well known is the hexaflexagon, made from equilateral triangles and folded into a hexagon. Another common type is the tetraflexagon, made from squares. There are others made from pentagons, hexagons and higher. Other types are made from non-equilateral triangles, rhombuses or rectangles. The Triangle Flexagon Bestiary gives an interesting selection of flexagons made from triangles.

There's a wide variety of possible flexes on these triangle flexagons. The Triangle Flexagon Flexes page lists some of them.

If you've played with making different flexagons, you may be interested to learn that some strips can actually be folded in multiple ways to create flexagons with different behavior.

All of these hinge along the edge between polygons. But a different type is the point flexagon, which flex across points instead.

Flexagons are perfect for an interesting assortment of puzzles. On the Flexagon Puzzle Page, I've assembled a collection of flexagon puzzles, including mazes, path puzzles, picture puzzles and a magic flexagon.