One of the mapping blogs I follow, CloudMade, turned up a cute little diversion in the form of a way to generate trihexaflexagons, where each of the three faces is a layer on the map: “hexaflexamaps”, so to speak. It’s a nice way to switch between (say) a cycle map, a topographic map, and a street map. OpenStreetMap is good for this, and is the basis for this diversion. Google could be used (with a rewrite) given that it has contour maps, street maps and satellite imagery. I think that the latter may not show up as well on a printout as the first two would.
Reading and playing with the result (a map of Newtown and area), inspired me to buy the new edition of Martin Gardner’s book of mathematical diversions containing flexagons. If you just want a map without all the hassle of hacking/running the Ruby script, the CloudMade blog entry has a pre-generated image of London, or you can use mine. Check CloudMade for instructions on folding.