Modular origami or unit origami is a
paperfolding technique which uses two or more sheets of paper to create a larger and more complex structure than would be possible 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, usually by inserting flaps into pockets created by the folding process. These insertions create tension or friction that holds the model together.
Definition and restrictions
Modular origami can be classified as a sub-set 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 not generally acceptable in modular origami.
The additional restrictions that distinguish modular origami from other forms of multi-piece origami are using many identical copies of any folded unit, and linking them together in a symmetrical or repeating fashion to complete the model. There is a common misconception that treats all multi-piece origami as modular.
More than one ''type'' of module can still be used. Typically this means using separate linking units hidden from sight to hold parts of the construction together. Any other usage is generally discouraged.
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'' (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
The Japanese kusudama (薬玉; lit. medicine ball) is a paper model that is usually (although not always) created by sewing multiple identical pyramidal units together using underlying geometric principles to form a spherical shape. Alternately th ...
'', 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 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 paperfolders include
Robert Neale, Sonobe,
Tomoko Fuse
Tomoko Fuse (, ''Fuse Tomoko'', born in Niigata, 1951) is a Japanese origami artist and author of numerous books on the subject of modular origami, and is by many considered as a renowned master in such discipline.
Fuse first learned origami wh ...
,
Kunihiko Kasahara,
Tom Hull,
Heinz Strobl and Ekaterina Lukasheva.
Types
Modular origami forms may be flat or three-dimensional. Flat forms are usually
polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two to ...
s (sometimes known as coasters), stars, rotors, and rings. Three-dimensional forms tend to be
regular polyhedra
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equival ...
or tessellations of simple polyhedra.
Modular origami techniques can be used to create lidded boxes which are not only beautiful but also useful as containers for gifts. Many examples of such boxes are shown in ''Fabulous Origami Boxes'' by
Tomoko Fuse
Tomoko Fuse (, ''Fuse Tomoko'', born in Niigata, 1951) is a Japanese origami artist and author of numerous books on the subject of modular origami, and is by many considered as a renowned master in such discipline.
Fuse first learned origami wh ...
.
There are some modular origami that are approximations of
fractals
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...
, 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
Tomoko Fuse (, ''Fuse Tomoko'', born in Niigata, 1951) is a Japanese origami artist and author of numerous books on the subject of modular origami, and is by many considered as a renowned master in such discipline.
Fuse first learned origami wh ...
's book ''Unit Origami-Multidimensional Transformations'' (published in 1990).
Modeling systems
Robert Neale's penultimate module
Neale developed a system to model
equilateral polyhedra based on a module with variable
vertex
Vertex, vertices or vertexes may refer to:
Science and technology Mathematics and computer science
*Vertex (geometry), a point where two or more curves, lines, or edges meet
* Vertex (computer graphics), a data structure that describes the positio ...
angles. Each module has two pockets and two tabs, on opposite sides. The angle of each tab can be changed independently of the other tab. Each pocket can receive tabs of any angle. The most common angles form polygonal faces:
* 60 degrees (
triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- colline ...
)
* 90 degrees (
square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
)
* 108 degrees (
pentagon)
* 120 degrees (
hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Regular hexagon
A '' regular hexagon'' has ...
)
Each module joins others at the vertices of a polyhedron to form a polygonal face. The tabs form angles on opposite sides of an edge. For example, a subassembly of three triangle corners forms a triangle, the most stable configuration. As the internal angle increases for squares, pentagons and so forth, the stability decreases.
Many polyhedra call for unalike adjacent polygons. For example, a
pyramid
A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilat ...
has one square face and four triangular faces. This requires hybrid modules, or modules having different angles. A pyramid consists of eight modules, four modules as square-triangle, and four as triangle-triangle.
Further polygonal faces are possible by altering the angle at each corner. The Neale modules can form any equilateral polyhedron including those having
rhombic faces, like the
rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron.
Properties
The rhombic dodecahed ...
.
Mukhopadhyay module
The Mukhopadhyay module can form any equilateral polyhedron. Each unit has a middle crease that forms an edge, and triangular wings that form adjacent stellated faces. For example, a cuboctahedral assembly has 24 units, since the
cuboctahedron
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it ...
has 24 edges.
Additionally,
bipyramids
A (symmetric) -gonal bipyramid or dipyramid is a polyhedron formed by joining an -gonal pyramid and its mirror image base-to-base. An -gonal bipyramid has triangle faces, edges, and vertices.
The "-gonal" in the name of a bipyramid does no ...
are possible, by folding the central crease on each module outwards or convexly instead of inwards or concavely as for the
icosahedron and other stellated polyhedra. The Mukhopadhyay module works best when glued together, especially for polyhedra having larger numbers of sides.
Notes and references
Bibliography
*
*
External links
3dOrigamiArt.comLearn how to 3d Origami, tutorials and artist network.
3D origami video tutorials by Arthur Vershigora.
Kusudama PicturesPhoto Gallery and Folding Instructions For Many Polyhedra and VariationsImage of Menger's Sponge in origamiModular origami pageOrigami GeospherePaper model of a Geodesic Sphere.
Oxi Module by Michał KosmulskiKusudama Me! Kusudamas of Lukasheva Ekaterina, also diagrams and tutorialsPaper Structures by Krystyna and Wojtek BurczykKusudama by Mikhail Puzakov & Ludmila Puzakova: models, folding instruction, history, geometry
{{DEFAULTSORT:Modular Origami
Modularity, Origami
Origami