Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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Analogues of the Cube
 
There are two different kinds of analogues in modular origami, surface analogues and method analogues.

Surface analogues are modular forms whose outer surfaces are distortions of each other (though the two forms can not necessarily be continuously distorted into each other in a mathematical way).

Method analogues are designs which share the same modular method.

The forms in the three sections below are all surface analogues of the cube (and thus of each other). Within the sections the designs are also method analogues of each other.

This page only shows a small selection of the known cube analogue designs.

 
Method Analogues of the 1- Fold Cube
 
  Name: The 1-Fold Cube - a design that can be loosely constructed on a flat surface but is not sufficiently stable to be picked up. It is therefore more of a multiple-piece than a modular design, but I include it here for the sake of completeness.

Modules / Paper shape / Folding geometry: 12 minimalist modules from squares using standard folding geometry.

Designer / Date: Kenneth Kawamura, 1977.

Diagrams: Diagrams were published in Kenneth Kawamura's booklet 'Meditations on a Waterbomb' in 1977.

 
  Name: The Butterfly Ball

Modules / Paper shape / Folding geometry: 12 very simple modules from squares using standard folding geometry.

Designer / Date: Kenneth Kawamura, early to mid 1970s.

Diagrams: Diagrams were published in Kenneth Kawamura's booklet 'Meditations on a Waterbomb' in 1977.

 
  Name: XYZ (12-part) - a twelve module version of Ed Sullivan's classic 6-part XYZ design.

Modules / Paper shape / Folding geometry: 12 modules using standard folding geometry.

Designer / Date: Independently discovered by at least Robert Neale, Michael Naughton and David Mitchell in the late 1980s. I do not know who has creative priority.

Diagrams: Diagrams can be found in Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4.

 
  Name: Enigma Cube (12-part )

Modules / Paper shape / Folding geometry: 12 modules from squares using standard folding geometry.

Designer / Date: David Brill, 1988.

Diagrams: In Paper Crystals - David Mitchell - Water Trade - ISBN 9780953477494.

 
Method Analogues of the Blintz Cube
 
  Name: The Harlequin Cube

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: Kenneth Kawamura in the early 1970's.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.

 
  Name: The Windmill Base Cuboctahedron - so named because the modules are obtained by partially opening out the folds of a standard windmill base.

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: I discovered this design in 1989. It has also been discovered by Michael Naughton. I do not know which of us has creaative priority.

Diagrams: Not yet available.

 
  Name: Robert Neale's Octahedron, Skeletal Octahedron or Nolid Octahedron

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: Robert Neale, mid 1960s. Many other paperfolders have independently originated this design , including Kunihiko Kasahara, also in the mid 1960's, slightly later than Robert Neale but on the other side of the world, and Joe Power, in Hawaii, sometime in the early to mid 1970's. Incorrectly attributed to Seiryo Takegawa in Origami Christmas Tree Decorations, Paul Jackson, BOS booklet 20, 1982.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.

 
  Name: The Harlequin Star aka Blue Balloon / Epsilon Star

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: Kenneth Kawamura, early to mid 1970s. Robert Neale also independently discovered this design at an early date. I do not know who has creative priority.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.

 
  Name: XYZ

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: Ed Sullivan, 1976.

Diagrams: Published in The Flapping Bird issue 25 in 1976.

 
  Name: Enigma Cube (6-part)

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1988.

Diagrams: In Paper Crystals - David Mitchell - Water Trade - ISBN 9780953477494.

 
Method Analogues of Paul Jackson's Cube
 
  Name: The Paul Jackson Cube.

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: Paul Jackson, early 1970's.

Diagrams: On-line diagrams can be found on the Modular Designs page of this site..

 
  Name: The Paul Jackson Cuboctahedron - produced by inverting all the corners of the Paul Jackson Cube to the mid-point of each edge.

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: Paul Jackson, shortly after discovering his eponymous cube, in the early 1970s.

Diagrams: Not yet available.

 
  Name: The Tetracube - which lie at the corner of one of the tetrahedra that could be inscribed within it. Unlike the Columbus Cube the Tetracube is a regular modular design. The Tetracube will also act as a macromodule.

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990.

Diagrams: In Building with Butterflies - David Mitchell - Water Trade - ISBN 978-0-9534774-7-0.

 
  Name: Metamorphosis - arrived at by applying the metamorphosis 1 distortion to one complete corner of the Paul Jackson Cube.

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990. In its final clean form the design is my own but it owes much to the earlier work of Iris Walker, Ricky Wong and Wayne Brown.

Diagrams: In Building with Butterflies - David Mitchell - Water Trade - ISBN 978-0-9534774-7-0.

 
  Name: Paper ball - a robust ball made by distorting all six corners of the Paul Jackson Cube. I made the ball in the picture in 1989 and have played keep it up tennis and catch with it on several occasions since. As you can see, it has survived quite well.

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1989.

Diagrams: Not yet available.

 
Method Analogues of the Sonobe Cube
 
  Name: The Sonobe Cube

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry. Cubes made from larger numbers of modules are also possible.

Designer / Date: Mitsonobu Sonobe, c1965.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.

 
  Name: The Sonobe 6-part 8-point Stubby Star / Convertible Cube

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry. Stubby Stars made from larger numbers of modules are also possible.

Designer / Date: David Mitchell, early 1990s.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.