Fold along dotted line...

...Scratch that. Make it "CNC routed line". Foldtex has created a foldable board that combines a stiff backer board with a flexible outer layer. All you have to do is CNC route out (yeah, real simple once you create the pattern file and find that CNC router you can rent) the stiff board and use the flexible material as a "hinge." They seem to think it will revolutionize how we think of fittings and corner connections. But amongst their awesome mobiles, sculptures, and party hats, I don't see an example of a practical application. Still, if you can fold it in paper, now you can make it out of wood and the face of your choice.