Imagine that we want to launch a satellite into space, which, once in orbit, will be powered by rigid solar panels that fan outward. But, to launch the satellite the panels have to be folded and compact. How would we design them?
In 1985, Koryo Miura, a Japanese astrophysicist, proposed a method of folding a flat surface into a smaller area: the Miura fold. This folds paper or other materials in such a way that allows each section to remain flat, which is a necessary condition for stiff materials like solar panels. These folds are considered to be shape-memory origami as after unfolding, the sheet can easily be re-folded and returned to its more compact shape, and hence the fold can be ‘remembered‘.
The Miura fold was used in Japan’s Space Flyer Unit, launched in 1995, and has “influenced the development of other folds that allow materials to be packed into a compact shape and then unfold in one continuous motion.”
The crease patterns of the Miura fold form a tessellation of the surface by parallelograms.
In one direction the creases lie along straight lines, where each parallelogram forms the mirror reflection of its neighbour along the crease. However, in the other direction, the creases zigzag and each parallelogram is the translation of its neighbour along the crease.
The Miura fold is a form of rigid origami: “the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat.“