Ever been frustrated by a paper map that, once unfolded, is impossible to figure out how to refold? The solution is the Miura-Ori sheet, which unfolds easily and naturally re-folds itself into a compact form:
Although this folding technique was first proposed (in a 1989 paper) by Japanese astrophysicist Koryo Miura to fold solar arrays for satellites, it is also perfect for paper maps. As explained at Eric Meltzer's blog (from where the above image was taken),
A Miura sheet has only one degree of freedom, and can be thought of as having only two states: fully open, or fully closed. Since reversing one fold in the sheet (that is, making a “mountain” into a “valley”) requires reversing all of the adjacent folds as well, the Miura sheet feels as though it has a memory, and is very resistant to deformation.
Despite Meltzer being "a loss as to why all maps aren’t folded this way" (he has a Kickstarter project to create a Miura tourist map for San Francisco), I'm certain I've seen and used such maps several times. (I'm pretty sure the RATP printed a pocket-size Métro/RER map that folded out like this.) When I was a backpacker in Europe in the early 90's, I recall that many of the local tourist maps folded this way, often with some first cardstock attached to two diagonally-opposite corner squares, both to serve as a protective cover for the map and as a "handle" for opening and closing the map. If you want to try and make such a map yourself, the folding technique is quite straightforward:
Eric Meltzer: The Miura-ori and how to fold it