# Miura fold

(Redirected from Miura map fold)
Crease pattern for a Miura fold. The parallelograms of this example have 84° and 96° angles.

The Miura fold (ミウラ折り Miura-ori?) is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Koryo Miura.[1]

The crease patterns of the Miura fold form a tessellation of the surface by parallelograms. In one direction, the creases of the pattern lie along straight lines, with each parallelogram forming the mirror reflection of its neighbor across each crease. In the other direction, the creases zigzag, and each parallelogram is the translation of its neighbor across the crease. Each of the zigzag paths of creases consists solely of mountain folds or of valley folds, with mountains alternating with valleys from one zigzag path to the next. Each of the straight paths of creases alternates between mountain and valley folds.[2]

The Miura fold is a form of rigid origami, meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat. This property allows it to be used to fold surfaces made of rigid materials; for instance, it has been used to simulate large solar panel arrays for space satellites in the Japanese space program.[3]

A folded Miura fold can be packed into a very compact 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. In the application to solar arrays, this property reduces the number of motors required to unfold this shape, reducing the overall weight and complexity of the mechanism.

Miura-ori

## References

1. ^ Forbes, Peter (2006), The Gecko's Foot: How Scientists are Taking a Leaf from Nature's Book, Harper Perennial, pp. 181–195.
2. ^ Bain, Ian (1980), "The Miura-Ori map", New Scientist. Reproduced in British Origami, 1981, and online at the British Origami Society web site.
3. ^ Nishiyama, Yutaka (2012), "Miura folding: Applying origami to space exploration", International Journal of Pure and Applied Mathematics 79 (2): 269–279.