Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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12-part Modular Designs
 
Cubes
 
  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 12-part Corner-pocket Sonobe Cube

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

Designer / Date: Not known.

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

Modules / Paper shape / Folding geometry: 12 assymetric corner-pocket Sonobe modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1995.

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

Modules / Paper shape / Folding geometry: 8 Mondrian modules (assymetric corner-pocket Sonobe modules) in two sets of four of different proportions combined with four standard Corner-pocket Sonobe modules. All from squares using standard folding geometry.

Designer / Date: David Mitchell, 2017.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: The Diagonally Banded Cube

Modules / Paper shape / Folding geometry: 12 modules from symmetric, asymmetric or doubly assymetric banded modules folded from various paper shapes.

Designer / Date: David Mitchell, 2001.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: The Broken Star Cube

Modules / Paper shape / Folding geometry: 12 Decorative Skew Sonobe modules from squares using sqrt5 folding geometry.

Designer / Date: David Mitchell, 1990.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: The Letterbox Tiled Diablo Cube

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

Designer / Date: David Mitchell, 2001.

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

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

Designer / Date: David Mitchell, 2001.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
8-point Stubby Stars
 
  Name: The Sonobe Alpha 12-part 8-point Stubby Star - many decorative variants are possible.

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

Designer / Date: Mitsonobu Sonobe, mid to late 1960s.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: The Sonobe Beta 12-part 8-point Stubby Star - many decorative variants are possible.

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

Designer / Date: David Mitchell, 2012.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: The Sonobe Corner-pocket module 12-part 8-point Stubby Star / Convertible Cube

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

Designer / Date: .

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: The Letterbox Alpha 8-point Stubby Star - many decorative variants are possible.

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

Designer / Date: David Mitchell, 1987

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: The Banded 8-point Star

Modules / Paper shape / Folding geometry: 12 modules from symmetric, asymmetric or doubly assymetric banded modules folded from various paper shapes.

Designer / Date: David Mitchell, 2001.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
Other designs
 
  Name: Gyroscope - a skeletal octahedron with a small hole in the centre. As the name implies, the Gyroscope can be used as an action toy.

Modules / Paper shape / Folding geometry: 12 modules in two sets of six from squares using standard folding geometry.

Designer / Date: Lewis Simon, c1970s

Diagrams: Not yet available.
 
  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: Dodecahedron

Modules / Paper shape / Folding geometry: 12 modules from silver rectangles.

Designer / Date: David Brill, 1980s.

Diagrams: In Brilliant Origami - David Brill - Japan Publications 1996 - ISBN 0870408968.
 
  Name: Dodecahedron - not particularly robust.

Modules / Paper shape / Folding geometry: 12 modules in sets of male/female pairs from squares using mock platinum folding geometry.

Designer / Date: David Mitchell, 1996.

Diagrams: In Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X.
 
  Name: Great Dodecahedron

Modules / Paper shape / Folding geometry: 12 modules in sets of male/female pairs from pentagons, each of which contributes a single vertex to the form.

Designer / Date: David Mitchell, 1990.

Diagrams: Not yet available.
 
  Name: Equilateral Pattern Tetrahedron

Modules / Paper shape / Folding geometry: 12 modules from silver rectangles using both standard and 60/30 degree folding geometry (though other rectangles of similar proportions could be used since the natural geometry of the silver rectangle is not utilised).

Designer / Date: David Mitchell, 1992.

Diagrams: British Origami Society Convention Pack Spring 1992.
 
  Name: Reptile Kite-pattern Tetrahedron

Modules / Paper shape / Folding geometry: 12 Reptile modules from squares using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 1997.

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

Modules / Paper shape / Folding geometry: 12 parallelogram modules from silver rectangles .

Designer / Date: Nick Robinson, 1986.

Diagrams: In Mathematical Origami - David Mitchell - Tarquin 1997 - ISBN 189961818X.
 
  Name: Rhombic Dodecahedron

Modules / Paper shape / Folding geometry: 12 triangle modules from silver rectangles .

Designer / Date: David Mitchell, 2004.

Diagrams: Not yet available.
 
  Name: Skeletal Cube or Nolid Cube

Modules / Paper shape / Folding geometry: 12 modules from silver rectangles .

Designer / Date: David Brill, 1980s.

Diagrams: In Mathematical Origami - David Mitchell - Tarquin 1997 - ISBN 189961818X
 
  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: Omega Star (12-part) - developed from the 12-part XYZ in exactly the same way as the original 6-part Omega Star was developed from the original 6-part XYZ.

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: 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.
 
  Name: ZYX (because of the similarity of the form to Ed Sullivan's XYZ)

Modules / Paper shape / Folding geometry: 12 modules from silver rectangles or similar using standrad folding geometry.

Designer / Date: David Mitchell, 1993.

Diagrams: Not yet available.
 
  Name: Alternative Artifact

Modules / Paper shape / Folding geometry: 12 in two sets of 6 modules, one set from squares using standard folding geometry and the other set from silver rectangles.

Designer / Date: David Mitchell, 1995.

Diagrams: Not yet available.
 
  Name: Three-Way Brick - can be linked into other similar bricks in all three directions. A rhombic dodecahedron from which twelve small rhombic pyramids have been removed.

Modules / Paper shape / Folding geometry: 12 modules in two sets of six from silver rectangles.

Designer / Date: David Mitchell, 1996.

Diagrams: Not yet available.
 
  Name: Proteus12

Modules / Paper shape / Folding geometry: 12 modules from squares using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 1992

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4.
 
  Name: Jitterbug - a modular origami version of the well known flexible toy of the same name (made from metal rods and rubber joints) which was designed by Buckminster Fuller. By twisting the pierced square faces of the form it is possible to collapse the cuboctahedron into an octahedron.

Modules / Paper shape / Folding geometry: 12 modules from squares using 60/30 degree folding geometry.

Designer / Date: Tung Ken Lam, 1990s.

Diagrams:
 
  Name: Skeletal Cuboctahedron (12-part) or Nolid Cuboctahedron (12-part)

Modules / Paper shape / Folding geometry: 12 modules from squares using 60/30 degree geometry.

Designer / Date: Tung Ken Lam

Diagrams:
 
  Name: Borromean Links

Modules / Paper shape / Folding geometry: 12 modules in 2 sets of 6 using standard folding geometry, based on division into fifths.

Designer / Date: David Mitchell, 1999. A version of Thoki Yenn's Umulius Rectangulum.

Diagrams: Not yet available.
 
  Name: Rhombicuboctahedron (12-part) - requires stiff paper.

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

Designer / Date: David Mitchell, 1989.

Diagrams: Not yet available.
 
  Name: Pierced Snub Cube

Modules / Paper shape / Folding geometry: 12 modules folded from bronze rectangles using 60/30 degree folding geometry

Designer / Date: Tung Ken Lam

Diagrams: Not yet available.
 
  Name: Duality

Modules / Paper shape / Folding geometry: 12 modules in 2 sets of 6 from squares using standard folding geometry.

Designer / Date: David Mitchell, 2016.

Diagrams: Not yet available.
 
  Name: Compound of Cube and Octahedron - made by adding hats to the Photoframe Cube.

Modules / Paper shape / Folding geometry: 12 modules in 2 sets of 6 from squares using standard folding geometry.

Designer / Date: David Mitchell, 2016.

Diagrams: Not yet available.
 
  Name: Andromeda is a skeletal octahedron whose edges have been developed into a twelve point star.

Modules / Paper shape / Folding geometry: 12 modules folded from squares using mock platinum folding geometry. 6 extra 'end cap' modules folded from squares using standrad folding geometry can be added to clad the central skeletal octahedron and produce the result shown in the photo.

Designer / Date: David Mitchell, 2012.

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4.