Thanks to those of you who have contacted me off list about this subject. Here is a first draft of an article which takes into account your suggestions.
I would like to add more about the work of Tomoko Fuse, but the difficulty is that she has written so many books and developed so many designs that I am rather spoilt for choice. Please let me know which of Tomoko's designs and books you particularly think ought to be mentioned. Thank you. You will see that I have mentioned a few of my own designs as well ... I haven't populated the section about books as yet. Suggestions please! I haven't added any references as yet. Do you think this is sufficiently accurate and comprehensive or not? What needs adding? What needs taking away? PS I take the list in digest form so responses won't be immediate! Dave Article begins Introduction: Modular origami is a two-stage paperfolding technique in which several, or sometimes many, sheets of paper are first folded into individual modules, or units, and then assembled into the final form of the design. Modular origami can be used to make both very simple and very complex forms. It can be used as a sculptural medium and to create action designs and toys. Modular origami is also of practical use in making polyhedral models. It is not necessary for all the modules used in making a design to be identical, although they often are. In Japan, modular origami is called yunnito origami (unit origami), a term invented by Kunihiko Kasahara. The two stages of folding and assembling the modules are not always completely separate. Sometimes the folding of the modules continues after they have been assembled. There is a related technique which also combines folded paper modules (of one particular kind only) to create (mostly) representational designs which is known as 3D Origami, Chinese Modular Origami or Golden Venture origami. History: In Japan, a modular cube called the 'Tematebako' (treasure chest) appears in a print in the book 'Ranma Zushiki' by Hayato Ohoka, which was published in 1734. It is thought to have been made from six modules, each of which is a Thread Container provided with tabs by means of cuts. In Western Europe a cube made by interlocking six folded playing cards, and usually therefore known as the Playing Card Cube, appears in a print from 1759, and fairly regularly thereafter. Despite these, and a few other, early examples, modular origami was not recognised as a distinct paperfolding technique until the 1960s. In the USA, the earliest published diagrams are for a two-piece ornament by John M Nordquist, from 1963, followed by diagrams for a two-piece 'Diamond' ornament by Betsy Kitsch, from 1964, and a series of two and three-piece designs of similar style by Molly Kahn in 1966. The most important impetus to the development of modular origami in this period, however, came from the publication of diagrams for a 'Color Box', a cube made from six identical modules, by Mitsunobu Sonobe, in 1968. Other Japanese paperfolders quickly realised that by combining other numbers of Sonobe modules, with only minimal alterations to the design, a much wider range of forms could be achieved. Kunihiko Kasahara in particular also developed bi-colour variations of the module. By this time there was frequent interaction between paperfolders in Japan and elsewhere in the world and knowledge of this module and its possibilities soon spread widely. Thereafter paperfolders in both Japan and the USA began to explore the wider possibilities of the modular origami technique and designs proliferated quickly.Ethics: Ethics: Modules are essentially individual single-sheet paperfolds and the same ethical considerations about cutting and decoration, their avoidance of their use, apply to them as apply to other single-sheet paperfolds. It is generally considered that modular assembles should hold together without the need for glue, tape or thread, but this opinion is not universally held. In the Japanese tradition, modular assemblies which resemble traditional kusudama (hanging balls of foliage or flowers) are frequently decorated with tassles. They are often also glued, or sewn, together. Forms: Modular assemblies come in many different forms, mostly, though not exclusively, geometrical in nature, including: Two-dimensional (flat) polygons, rings, stars, and rotors. Two-dimensional mats (sometimes known as quilts) which are in theory infinitely extensible in all directions. Bowls, boxes and other containers. Polyhedra models. These come in many varieties. They may have flat faces, or have faces that are either dimpled (faceted inwards) or pimpled (faceted outwards), have faces missing, or have a combination of any of these. Modular sculptures. These are designs based upon an underlying polyhedral form which have been developed to produce a sculptural form. Modular sculptures that resemble balls of flowers are often called kusudama. Action designs and toys: Designs where the modules can move in relation to each, without falling apart, so that the shape of the design changes in some way e.g, by collapsing into a different shape, or where the form allows them to be used as toys, like spinners or rolling wheels. Folding Geometries and Starting Shapes: The majority of modular designs, particularly early modular designs such as the Sonobe module and its many variations are based on standard 90 / 45 / 22.5 degree folding geometry. However, it is also quite common to find designs based on 120 / 60 / 30 degree folding geometry, 109.28/70.32/54.84/35.36 degree folding geometry or 108/72/36 degree folding geometry. Some modular paperfolding designers, generally those who prefer to start from squares, construct these angles, or close approximations thereof, using mathematical references. Other designers prefer to start with rectangles that naturally yield the required angles when folded. The 1:sqrt2, or silver, rectangle, for instance, naturally yields angles of 109.28/70.32/54.84/35.36 degrees. Assembly systems: The original Sonobe module is folded to produce a parallelogram shape that has two central pockets and two outside tabs. When the modules are assembled, the tabs of one module fit inside the pockets of two others. The tab and pocket system is the most common assembly system used in modular design but there are others, such as compact weave and compression systems. In a compact weave design the modules have no tabs or pockets but are assembled so that part (normally half) the module goes outside of, and part (normally the other half) inside of adjacent modules. The stability of this assembly system depends entirely on the overall shape of the form. A mutual compression design relies on the resilience of paper to compression. Effectively, a part of each module is compressed slightly by being inserted between one of more adjacent modules, which in turn are compressed by others etc. The resistance of the paper to this compression locks the design together. Surface patterns: There are three different ways to pattern the surface of a modular design. The easiest, and most obvious, is to combine modules folded from paper of different colours. The second is to use bi-colour paper (paper which is a different colour or pattern on each surface) so that the surface of each module is itself divided into differently coloured, or patterned areas. The third method is to combine the first two techniques. Paper: In general there is no type of paper that is better than any other for practicing modular origami. The art is to find the paper that is ideal for the particular design you are folding and constructing. However, modules designed to pattern the surface of the design in bi-colour patterns will usually need to be folded from bi-colour paper. Some classic modular origami designs: The Tematebako - a cube made from six Thread Containers (aka Menko or Puzzle Purses) which have been provided with tabs by means of cutting slits into the centre of the design. The Playing Card Cube - a cube made from six playing cards (or nowadays often business cards) which have been folded into simple modules. John Nordquist's 'Ornament' - a simple hanging ornament made by combining two modules folded from two 2x3 rectangles. Mitsunobu Sonobe's 'Color Box' - a cube made from six identical tab and pocket modules folded from squares. This module is commonly known as the Sonobe module. A version of the module which has the corners inverted to create pockets at the corners, rather than in the centre as in the original module, was developed by Tomoko Fuse. Robert Neale's 'Octahedron' - a compact weave design assembled from six modules folded from squares. The form of the octahedron is represented by three interpenetrating square planes. Robert Neale's 'Magic Star' - a flat, shape-changing, action design assembled from eight modules folded from squares. An octagonal rotor transforms to a ring and back again. Robert Neale's 'Penultimate Dodecahedron' - a modular sculpture based on the form of a dodecahedron made from thirty identical modules folded from squares. E D Sullivan's 'XYZ' - a form composed of three intersecting squares arranged like the x, and z axes of simple mathematical space, assembled from six modules folded from squares. Philip Shen's 'Omega Star' - a 12-pointed star developed from E D Sullivan's 'XYZ'. A good example of a design where the folding continues after the modules have been assembled. Kenneth Kawamura's 'Butterfly Ball' - a delicate structure made of twelve 'butterfly' modules that can be thrown in the air and hit with the hand so that the 'butterflies' fly apart and flutter to the floor. Kenneth Kawamura's 'Harlequin Star' - a compact weave design made from six simple modules. The inverse of Robert Neale's 'Octahedron'. Paul Jackson's 'Cube' - a flat-faced cube assembled from six modules folded from squares. A good example of a design that relies on mutual compression to hold it together. Minako Ishibashi's 'Brocade' - a design made from six variations of the Fuse version of the Sonobe module that appears to be surrounded by ribbons of paper. Nick Robinson's 'Rhombic Dodecahedron' - a flat faced rhombic dodecahedron assembled from twelve modules folded from silver rectangles. The module is a development of the Sonobe module achieved by changing the folding geometry. Hiroshi Kumasaka's 'Joyful Units' (aka the Rotunda) - a rotating ring made from eight simple units folded from squares. Hachiro Kamata's 'Star Decorative Ball' - a ball decorated with raised stars assembled from 30 modules folded from squares. David Mitchell's 'Electra' and 'Electra60' - modular sculptures made from thirty and sixty identical modules respectively. David Mitchell's '6-part Stellated Rhombic Dodecahedron' - a flat-faced stellated rhombic dodecahedron assembled from six modules folded from silver rectangles. David Brill's '12-part Enigma Cube' - reworking using twelve identical curved modules of a 2-part design by David Mitchell. Tom Hull's 'Five Intersecting Tetrahedra' - a compound design made by interweaving five open-frame tetrahedra. Each tetrahedra is assembled from four modules folded from 3x1 rectangles. The open-frame tetrahedron design was independently discovered by both Tomoko Fuse and Francis Ow. Books on modular origami Not populated as yet. Ends
