The 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 Kōryō Miura. The crease patterns of the Miura fold form a

tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety ...

of the surface by

parallelogram In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram a ...

s. In one direction, the creases 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 Translation is the communication of the semantics, meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The English la ...

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.. Reproduced in ''British Origami'', 1981, and online at the British Origami Society web site. The Miura fold is related to the Kresling fold, the Yoshimura fold and the Hexagonal fold, and can be framed as a generalization of these folds. 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, making it distinct from the Kresling fold and Yoshimura fold which cannot be rigidly folded and require panel deformations to compress to a compact state. For instance, large

solar panel A solar panel is a device that converts sunlight into electricity by using photovoltaic (PV) cells. PV cells are made of materials that produce excited electrons when exposed to light. These electrons flow through a circuit and produce direct ...

arrays for space satellites in the Japanese space program have been Miura folded before launch and then spread out in space. A folded Miura fold can be packed into a compact shape, its thickness reflecting only the thickness of the folded material. Folded material can be unpacked in one motion by pulling on its opposite ends, and likewise folded by pushing the two ends together. In the solar array application, this property reduces the number of

motor An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power gene ...

s required to unfold this shape, reducing weight and complexity.

Applications

The 1996

Space Flyer Unit The was a spacecraft which was launched by Japan on March 18, 1995.
Main Reference

Technical dat ...

deployed the 2D Array from a Miura folded configuration. The inflatable membrane structure of the SPROUT satellite is carried into space in the Miura-folded state, and then deployed using inflatable tubes themselves carried into space in the Octagon-folded state. Other potential applications of this fold include surgical devices such as

stent In medicine, a stent is a tube usually constructed of a metallic alloy or a polymer. It is inserted into the Lumen (anatomy), lumen (hollow space) of an anatomic vessel or duct to keep the passageway open. Stenting refers to the placement of ...

s and flat-foldable furniture. Researchers at the

University of Fribourg The University of Fribourg (; ) is a public university located in Fribourg, Switzerland. The roots of the university can be traced back to 1580, when the notable Jesuit Peter Canisius founded the Collège Saint-Michel in the City of Fribourg ...

used the Miura fold to stack

hydrogel A hydrogel is a Phase (matter), biphasic material, a mixture of Porosity, porous and Permeation, permeable solids and at least 10% of water or other interstitial fluid. The solid phase is a water Solubility, insoluble three dimensional network ...

films, generating electricity similarly to

electric eel The electric eels are a genus, ''Electrophorus'', of neotropical freshwater fish from South America in the family Gymnotidae, of which they are the only members of the subfamily Electrophorinae. They are known for their electric fish, ability ...

s. The Miura fold is used to cause many parts of the stack to contact each other simultaneously.

References

External links

Tessellation And Miura Folds - Science Friday
Paper folding Japanese inventions {{Mathematics of paper folding