Flexagons - another fun-math connection

Last Thursday's piece about Playfulness, Invention and Mathematical Thought set me thinking about all the fun things I've done that belong to this math-fun connection. Which reminded me about one of the most mystifyingly magically mathishly fun toys I've so far encountered - the flexagon.

It's a thing you make out of a folded paper strip that's divided into triangles. You fold and fold until you get something that looks like a hexagon. You glue one of the edges and get this ever-unfolding thing. Then you go so far as to draw pictures and stuff on this ever-unfolding thing, and when you ever-unfold it, the pictures change and change and, well, change. It's kinda like a folded moebius strip. Which is also amazing, fun, and ticklishly puzzling. And it's the ticklishly puzzling part that makes this whole thing so mathematical.

The hexahexaflexagon is no secret. There are many World Wide pages devoted to its mysteries. This site includes a cool Java simulation of a hexahexaflexagon flexing hexishly. This site gives instructions for building tri-, tetra-, penta-, and, of course, hexahexaflexagons. And here we even get hexahexaflexagon-making software.

Flex on, dude!