Rigid origami is a branch of origami

Origami

is the traditional Japanese art of paper folding, which started in the 17th century AD at the latest and was popularized outside Japan in the mid-1900s. It has since then evolved into a modern art form...

 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

Mathematics of paper folding

The art of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability and the use of paper folds to solve mathematical equations.-Flat folding:The construction of origami models is sometimes shown as crease...

, it can be considered as a type of mechanical linkage

Linkage (mechanical)

A mechanical linkage is an assembly of bodies connected together to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for...

, 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 bag

Shopping bag

Shopping bags are medium sized bags, typically around 10-20 litres in volume , that are often used by grocery shoppers to carry home their purchases...

s with flat bottoms and airbag

Airbag

An Airbag is a vehicle safety device. It is an occupant restraint consisting of a flexible envelope designed to inflate rapidly during an automobile collision, to prevent occupants from striking interior objects such as the steering wheel or a window...

s are studied as part of rigid origami.

Mathematics

The number of standard origami bases that can be folded using rigid origami is restricted by its rules.

Rigid origami does not have to follow the Huzita–Hatori axioms, the fold lines can be calculated rather than having to be constructed from existing lines and points. However Kawasaki's theorem

Kawasaki's theorem

Kawasaki's theorem is a theorem in the mathematics of paper folding, named after Toshikazu Kawasaki, that gives a criterion for determining whether a crease pattern with a single vertex may be folded to form a flat figure.- Statement of the theorem :...

 and Maekawa's theorem are still applicable.

The Bellows theorem says that a flexible polyhedron

Flexible polyhedron

In geometry, a flexible polyhedron is a polyhedral surface that allows continuous non-rigid deformations such that all faces remain rigid. The Cauchy rigidity theorem shows that in dimension 3 such a polyhedron cannot be convex .The first examples of flexible polyhedra, now called Bricard's...

 has constant volume when flexed.
The napkin folding problem

Napkin folding problem

The napkin folding problem in geometry explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis, and the Arnold's rouble problem referring to...

 asks whether it is possible to fold a square so the perimeter of the resulting flat figure is increased. That this can be solved within rigid origami was proved by A.S. Tarasov in 2004.

Applications

The Miura fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites.

Robert J. Lang

Robert J. Lang

Dr. Robert J. Lang is an American physicist who is also one of the foremost origami artists and theorists in the world. He is known for his complex and elegant designs, most notably of insects and animals. He has long been a student of the mathematics of origami and of using computers to study the...

 has applied origami to the problem of folding airbag

Airbag

An Airbag is a vehicle safety device. It is an occupant restraint consisting of a flexible envelope designed to inflate rapidly during an automobile collision, to prevent occupants from striking interior objects such as the steering wheel or a window...

s

and to folding a space telescope.
Folding paper shopping bag

Shopping bag

Shopping bags are medium sized bags, typically around 10-20 litres in volume , that are often used by grocery shoppers to carry home their purchases...

s is a problem where the rigidity requirement means the classic solution does not work.

Recreational uses

Martin Gardner

Martin Gardner

Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...

 has popularised flexagon

Flexagon

In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front....

s which are a form of rigid origami and the flexatube.