A Universal Crease Pattern for Folding Orthogonal Shapes

We present a universal crease pattern—known in geometry as the tetrakis tiling and in origami as box pleating—that can fold into any object made up of unit cubes joined face-to-face (polycubes). More precisely, there is one universal finite crease pattern for each number n of unit cubes that need to be folded. This result contrasts previous universality results for origami, which require a different crease pattern for each target object, and confirms intuition in the origami community that box pleating is a powerful design technique.