David Mitchell's Origami Heaven - Modular Origami - Hexoids
 
Hexoids

A selection of designs made by combining six identical modules.

 
  The Sonobe Cube was discovered in about 1965 by the Japanese paperfolder Mitsonobu Sonobe and is one of the two pillars on which the development of modular origami rests (the other being Robert Neale's Octahedron). The Sonobe Cube is the base form of the Sonobe module sub-set of the centre-pocket modular family. In its construction, it is very similar to the Mystery Box

On-line diagrams

     
  The PJ Tetracube is developed by inverting four corners of Paul Jackson's Cube (which must be chosen to correspond to the vertices of a tetrahedron inscribed within the cube) to the mid-point of the adjacent edges. The PJ Tetracube will function as a macro-module in a similar way to the Columbus Cube. The Tetracube form was independently originated by several paperfolders. It is not known who got there first.

Ref: M1048 / Diagrams can be found in Building with Butterflies - David Mitchell - Water Trade 1999- ISBN 095347741X

     
  Robert Neale's Octahedron is one of the twin pillars of modular origami in the modern era (the, of course, other being the Sonobe module and cube). The design has also yielded an impressive array of variations and developments.

Ref: XM1041 / Diagrams can be found in Mathematical Origami - David Mitchell - Tarquin 1997 - ISBN 189961818X

     
  The Harlequin Star is made from six modules in the form of slightly flattened preliminary folds. It is a very delicate construction and takes care and patience to assemble. Once assembled however it is sufficiently stable to stand up to careful handling. Both Robert Neale and Kenneth Kawamura independently discovered this design at an early date. It is not known who got there first.

Ref: XM1040

     
  Robert Neale's Cube Analogue Rhombicuboctahedron is a classic of simple modular origami design. There are two versions of the module, based on the 3x3 and 4x4 grids respectively. Michael Naughton (who calls the design the Multi-Ball) has pointed out that there are an infinity of related cube analogues eight of whose rectangular faces are oblong rather than square.

Ref: XM1050 / Diagrams not yet available.

     
  4-Cubes is an elegant hexoid that can be viewed either as four cubes joined edge to edge or as a single large cube from which four smaller cube-shaped sections have been removed. The design is not only aesthetically pleasing but also particularly satisfying to fold and assemble.

Ref: M1030 / Diagrams not yet available.

     
  David Mitchell's Enigma Cube is a curious but attractive sculpture in the form of a cube surrounded by curved collars. Several modular methods are known but the 6-part version shown here, developed from Ed Sullivan's XYZ, is in many ways the most interesting, particularly in the way that the form continues to develop after the modules have been assembled.

Ref: M1005 / Diagrams can be found in Paper Crystals - David Mitchell - Water Trade 2000 - ISBN 0-9534774-2-8

     
  David Mitchell's 6-part Truncated Tetrahedron is made by weaving together six extremely simple modules folded from a bronze rectangles, although the necessary geometry can, of course, be embedded into any other shape of paper. Tomoko Fuse has independently produced a similar design using modules folded from a square.

Ref: M1071 / Diagrams not yet available.

     
  The Double Kite Pattern Tetrahedron is made using six modules each of which contributes two of the kite-shaped regions of colour. The design can be made from Davis Mitchell's Simplified Terada Edge modules or by using Terada Edge modules in their original form.

Ref: M1139 / Diagrams for ST module designs not yet available.

     
  Six of the faces of Tung Ken Lam's remarkable Pierced Icosahedron are missing, a property which allows the construction of the form using just six modules. The design can function as a mathematical model demonstrating that the icosahedron can be seen as a snub tetrahedron, the missing faces being those of the tetrahedron in question.

Ref: XM1145 / Diagrams not yet available.

     
 

David Mitchell's Icarus Cube is a decorative variation of Paul Jackson's Cube in which the centre of the square is brought out to form a transverse wing across the centre of the face.

M1099 / Diagrams can be found in Building with Butterflies - David Mitchell - Water Trade 1999- ISBN 095347741X

   
  Natale Fietta's 3-Way Joint is an unusual hexoid worthy of a better name. The proportions of the design can easily be varied by folding the modules from 6x4 or 7x5 etc rectangles, or from a square divided into a 5x5, 6x6 or 7x7 etc grid and beginning by folding two opposite edges inwards to achieve the rectangle required.

Diagrams can be found in the British Origami Society convention pack for Spring 1989.

     
  David Mitchell's Omicron is a simple but attractive hexoid in the form of a large cube with one eighth size cubes removed from each corner. It can also be seen as composed of six 4x2x1 cuboids. Versions with other proportions are possible.

M1098 / Diagrams not yet available.

     
  David Mitchell's Upsilon is a simple but attractive hexoid in the form of a cube each of whose sides has been extended to a point in two opposite directions.

M1120 / Diagrams not yet available.

     
  David Mitchell's Semi-Star is a strange twelve pointed star developed from Robert Neale's Octahedron by folding the outer layers of the form outwards to create the points. The name arises from the fact that only half of each point is present in the design. This form was subsequently developed into Andromeda, in which the points are complete.

M1121 / Diagrams not yet available.

     
  David Mitchell's Combination Silverhedron 2 is an unusual hexoid made by combining six modules developed from the traditional fold known as the Pinwheel. The square and silver triangle faces are flat while the equilateral faces are dimpled. In this form the edges of the square faces are shorter than the edges of the equilateral faces. Left and right-handed versions are possible.

Ref: M1128 / Diagrams not yet available.

     
  The form of David Mitchell's Waterbomb Star is achieved by adding a waterbomb base to each face of a cube (in such a way that the tips of the arms of the waterbomb base meet each other at the corners of the underlying cube). The module is particularly elegant and pleasing to fold.

M1027 / Diagrams not yet available.

     
  David Mitchell's Ethereal is a hanging sculpture that will delight modular aficionados with the delicate elegance of its design. The overall form is that of an octahedron (each of whose faces has been divided into four equal regions, then dimpled). The original form of the module was provided with tabs and pockets, but in this form it proved impossible to assemble the design.

Ref: M1028 / Diagrams not yet available.

     
  David Mitchell's Gaia is a decorative pierced rhombicuboctahedron assembled from six modules derived from the Enigma Fold. The complex final form is largely developed after the modules have been assembled.

Ref: M1006 / Diagrams can be found in British Origami Society Convention Pack Spring 1996 (module only) and Origami Munchen Convention Pack July 1995

     
  The angles required to model David Mitchell's Rotating Ring of Six Tetrahedra are not those normally required for modular origami designs. It is therefore somewhat surprising that they come so easily from the natural folding geometry of the square.

Ref: M1111 / Diagrams not yet available.

     
  Jun Maekawa's Dodecahedron is a wonderful example of a hexoid. Each of the six modules contributes two complete linked pentagonal faces to the design, which are are then assembled using a clever flap and pocket system.

Ref: M1097 / Diagrams can be found in Origami for the Connoisseur - Kunihiko Kasahara and Toshie Takahama - Japan Publications 1987 - ISBN 087040670.

     
  Although discovered entirely independently, David Mitchell's Artifact is closely related to David Brill's Waterbombic Dodecahedron. The form is identical and the modules are essentially similar, except that in Artifact six,rather than just three, modules are required. Artifact is used as a macro-module in David Mitchell's Stargate and Nexus designs.

Ref: M1061 / Diagrams not yet available.

     
  Thought by many to be David Mitchell's greatest modular design, the 6-part Stellated Rhombic Dodecahedron is remarkable for the way in which every detail of the module comes so naturally from the folding geometry of the silver rectangle.

Ref: M1010 / Diagrams can be found in Wonderful World of Modulars - Tomoko Fuse - ISBN 4-405-07553-0

     
  This complex seeming sculpture, known as Darkstar, is in fact a simple hexoid. The modules are folded from silver rectangles using the natural folding geometry of the shape.The sculpture has narrow slits in the sides of the points where two raw edges of the paper meet and therefore works much better in black than in any other colour.

Ref: M1033 / Diagrams not yet available.