thumb|Triangle Edge [[Icosahedron designed by Bennett Arnstein. Diagrammed in the book 3-D Geometric Origami: Modular Polyhedra (1995)]]
thumb|An example of golden venture folding.
thumb|Modular origami hexagonal box with six-petal lid. Designed by [[Tomoko Fuse.]]
[[File:A page from Ranma zushiki 欄間図式 Volume 3 (1734).jpg|thumb|The page from Ranma zushiki 欄間図式 Volume 3 (1734) where modular origami models are depicted. This is usually done by inserting flaps into pockets created by the folding process, which create tension or friction and hold the model together.
Definition and restrictions
thumb|Models made from the indicated number of [[Sonobe units.]]
Modular origami can be classified as a subset of multi-piece origami, since the rule of restriction to one sheet of paper is abandoned. However, all the other rules of origami still apply, so the use of glue, thread, or any other fastening that is not a part of the sheet of paper is generally unacceptable in modular origami.
Not all multi-piece origami is modular, as modular origami must involve linking identical copies of a module in a symmetrical or repeating fashion. However, linking units, which are hidden from sight to hold parts of the construction together are acceptable. Any other usage of non-identical modules are generally discouraged.
History
thumb|right|A [[kusudama, the traditional Japanese precursor to modular origami]]
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 (magic treasure chest).
Isao Honda's World of Origami (published in 1965) appears to have the same model, where it is called a "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 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 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 US and later by Mitsunobu Sonobe in Japan. The 1970s saw a sudden period of interest and development in modular origami as its own distinct field, leading to its present status in origami folding. One notable figure is Steve Krimball, who discovered the potential in Sonobe's cube unit and demonstrated that it could be used to make alternative polyhedral shapes, including a 30-piece ball.
Since then, the modular origami technique has been popularized and developed extensively, and now there have been thousands of designs developed in this repertoire.
Notable modular origami artists include Robert Neale, Mitsunobu Sonobe, Tomoko Fuse, Kunihiko Kasahara, Tom Hull, Heinz Strobl, Rona Gurkewitz, Meenakshi Mukerji, and Ekaterina Lukasheva.
Types
thumb|Modules of modular origami
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 tessellations of simple polyhedra.
Modular origami techniques can be used to create a wide range of lidded boxes in many shapes. Many examples of such boxes are shown in Tomoko Fuse's books Origami Boxes (1989), Fabulous Origami Boxes (1998), and Tomoko Fuse's Origami Boxes (2018).
There are some modular origami that are approximations of fractals, such as Menger's sponge. 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 described in Tomoko Fuse's 1990 book Unit Origami-Multidimensional Transformations.