What is the Miura fold and rigid origami?

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Rigid origami:
Is a branch of origami which is concerned with folding structures using flat rigid sheets joined by hinges. It is a part of the study of the mathematics of paper folding, it can be considered as a type of mechanical linkage, and has great practical utility. For instance it was used in the construction of large solar panel arrays that have to be folded before deployment. There is no requirement that the structure start as a flat sheet — for instance shopping bags with flat bottoms and airbags are studied as part of rigid origami.


The Miura fold
Is a rigid fold that has been used to simulate large solar panel arrays for space satellites in the Japanese 1995 Space Flight Unit. It was invented by Japanese astrophysicist Koryo Miura. It is an example of the practical importance of rigid origami, or treating hinges and rigid surfaces like the paper and creases in paper folding problems.

A folded Miura fold can be packed into an area no larger than the size of one of the segments that make up the overall shape, its thickness restricted only by the thickness of the folded material.

The fold can also be unpacked in just one motion by pulling on opposite ends of the folded material, and likewise folded again by pushing the two ends back together. This was beneficial to the aforementioned solar array as it reduced the number of motors required to unfold it, reducing the overall weight and complexity of the mechanism.