Flexagons are neat little paper models that can be folded in different ways to show different surfaces. There are dozens of different types, and this site gives a good overview & patterns.

So, besides a fun plaything, what else can you do with it?

You can take a regular flat maze and draw it on a pyramid flexagon (pictured at right) instead. To follow the maze, you must fold the puzzle in the correct way.

Or, you can use a tetra-tetra flexagon, like Britta Gustafson did to make a beautiful map (below) that folds to reveal different levels of detail.
(See also this instructable, for an even-more detailed step-by-step guide)

So, what ideas can you think of for this? If you’re a spy, you could combine all of your fake identification documents in to one, so you’ll be ready to show the proper one whenever needed. Not a spy? Then how about combining all your grocery store loyalty cards in to one object?

Bonus: watch this video for a very fun Flexagon (feel free to skip to 3:00, where Arvind Gupta demonstrates it). The video shows how to make it, but a printed version would be easier to follow — can anyone find more information about this?