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,

Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...

ese astrophysicist

Kōryō Miura Kōryō Miura ( ja, 三浦公亮, born 1930) is a Japanese astrophysics, astrophysicist, inventor, and origamist known for the Miura fold. He is a professor emeritus at the University of Tokyo and at the Institute of Space and Astronautical Scie ...

. The

crease pattern A crease pattern is an origami diagram that consists of all or most of the creases in the final model, rendered into one image. This is useful for diagramming complex and super-complex models, where the model is often not simple enough to diagram e ...

s of the Miura fold form a

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

of the surface by

parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equa ...

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 Meaning (linguistic), 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 ...

of its neighbor across the crease. Each of the zigzag paths of creases consists solely of

mountain fold A mountain is an elevated portion of the Earth's crust, generally with steep sides that show significant exposed bedrock. Although definitions vary, a mountain may differ from a plateau in having a limited Summit (topography), summit area, and ...

s or of

valley fold A valley is an elongated low area often running between Hill, hills or Mountain, mountains, which will typically contain a river or stream running from one end to the other. Most valleys are formed by erosion of the land surface by rivers ...

s, 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 Kresling fold is a folding pattern which naturally arises under torsional load. It is named after Biruta Kresling, a Paris-based architect born in Berlin in 1942, who has published extensive research deployable structures, and in particular on ...

, the

Yoshimura fold In mathematics, the Schwarz lantern is a polyhedral approximation to a cylinder, used as a pathological example of the difficulty of defining the area of a smooth (curved) surface as the limit of the areas of polyhedra. It is formed by stack ...

and the Hexagonal fold, and can be framed as a generalization of these folds. The Miura fold is a form of

rigid origami Rigid origami is a branch of origami which is concerned with folding structures using flat rigid sheets joined by hinges. That is, unlike in traditional origami, the panels of the paper cannot be bent during the folding process; they must remain ...

, 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

and

which cannot be rigidly folded and require panel deformations to compress to a compact state. For instance, large

solar panel A solar cell panel, solar electric panel, photo-voltaic (PV) module, PV panel or solar panel is an assembly of photovoltaic solar cells mounted in a (usually rectangular) frame, and a neatly organised collection of PV panels is called a photo ...

arrays for space satellites in the

Japanese space program The Japanese space program ( ja, 日本の宇宙開発) originated in the mid-1950s as a research group led by Hideo Itokawa at the University of Tokyo. The size of the rockets produced gradually increased from under at the start of the proje ...

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 gen ...

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 metal or plastic tube inserted into the lumen of an anatomic vessel or duct to keep the passageway open, and stenting is the placement of a stent. A wide variety of stents are used for different purposes, from expandab ...

s and flat-foldable furniture. Researchers at the

University of Fribourg The University of Fribourg (french: Université de Fribourg; german: Universität Freiburg) 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 ...

used the Miura fold to stack

hydrogel A hydrogel is a crosslinked hydrophilic polymer that does not dissolve in water. They are highly absorbent yet maintain well defined structures. These properties underpin several applications, especially in the biomedical area. Many hydrogels ar ...

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. They are known for their ability to stun their prey by generating electricity, delivering shocks at up to 860 volts ...

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

References

External links

Origami science
Paper folding Japanese inventions {{Mathematics of paper folding