Modular origami

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A stellated icosahedron made from custom papers.

Modular origami, or unit origami, is a paperfolding technique which uses multiple sheets of paper to create a larger and more complex structure than would be feasible using single-piece origami techniques. Each individual sheet of paper is folded into a module, or unit, and then modules are assembled into an integrated flat shape or three-dimensional structure by inserting flaps into pockets created by the folding process. These insertions create tension or friction that holds the model together.

1 Definition and Restrictions
2 History
3 Types of Modular Origami
4 Notable Modular Paperfolders
5 External links

[edit] Definition and Restrictions

Modular origami can be viewed as a sub-set of multi-piece origami, and therefore the rules of origami still apply, although the usual convention of restriction to one piece of unaltered paper is temporarily ignored. However, the use of glue, thread, or any other fastening that is not a part of the sheet of paper is not generally acceptable in modular origami.

Examples of modular origami made up of Sonobe units.

One of the defining elements of modular assemblies is that they are always made from one or more sets of identical modules. There is a common misconception that treats all multi-piece origami as modular, but this is not the case. However, modular origami can use more than one type of module, but generally any of this use other than connectors is frowned upon.

Modular origami forms may be flat or three-dimensional. Flat forms are usually polygons (sometimes known as coasters), stars, rotors and rings. Three-dimensional forms tend to be regular polyhedra or tesselations of simple polyhedra.

There are some modular origami that are fractals, such as Menger's sponge, which can only be approximated in origami.

[edit] History

The first historical evidence for a modular origami design comes from a Japanese book by Hayato Ohoka published in 1734 called Ranma Zushiki. It contains a print that shows a group of traditional origami models, one of which is a modular cube. The cube is pictured twice (from slightly different angles) and is identified in the accompanying text as a tamatebako or 'magic treasure chest'.

A Kusudama, the traditional Japanese precursor to modular origami.

Isao Honda's 'World of Origami' (Japan Publications ISBN 0-87040-383-4 published in 1965) appears to have the same model, where it is called the 'Cubical Box'. The six modules required for this design were developed from the traditional Japanese paperfold commonly known as the Menko. Each module forms one face of the finished cube.

There are several other traditional Japanese modular origami designs, including balls of folded paper flowers known as kusudama, or medicine balls. These designs are not integrated and are commonly strung together with thread. The term kusudama is sometimes, rather inaccurately, used to describe any three-dimensional modular origami structure resembling a ball.

There are also a few modular designs in the Chinese paperfolding tradition, notably the Pagoda (from Maying Soong) and the Lotus made from Joss paper.

Most traditional designs are however single-piece and the possibilities inherent in the modular origami idea were not explored further until the 1960s when the technique was re-invented by Robert Neale in the USA and later by Mitsonobu Sonobe in Japan. Since then the modular origami technique has been popularised and developed extensively and there are now many thousands of designs in the repertoire.

[edit] Types of Modular Origami

Macro-modular origami is a form of modular origami in which finished assemblies are themselves used as the building blocks to create larger integrated structures. Such structures are taught in Tomoko Fuse's book Unit Origami-Multidimensional Transformations (Japan Publications ISBN 0-87040-852-6 published in 1990) Another book about modular origami is GeoGami.

Anything can be represented by using sonobe units. Simply refold the tabs up or down to make any shape. Go to http://www.math.lsu.edu/~verrill/origami/tetraunit/sonobe1.gif for instructions on folding this unit,and http://www.math.lsu.edu/~verrill/origami/tetraunit/sonobe2.gif for instructions on assembly.