Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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Modular Sculptures
 
Modular sculptures are any abstract geometric modular design that are neither straightforward mathematical models or kusudamas. They can be simple designs made from just two modules or quite complex designs made from sixty modules or more, but in either case they are necessarily based on, and developed from, an underlying polyhedral structure. Some modular sculptures will also function as macromodules that can be combined into larger macromodular sculptures.

Many modular sculptures are good examples of partnership art, a concept that expresses the partnership that often exists in origami/paperfolding between the designer, who first conceptualises and defines the design, and the folder, who realises one expression of it at one particular point in time, so that both contribute in equal partnership to the finished work.

I also sometimes use the term paper crystal as a synonym for modular sculpture. Paper Crystals is also the title of a book which contains folding diagrams for many of the best of my designs in this category.

Larger pictures of many of my own modular sculpture designs can be found in the Gallery of Paper Crystal Sculpture.
 
 
 
  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.
 
  Name: Andromeda 60

Modules / Paper shape / Folding geometry: 60 modules folded from squares using mock platinum folding geometry.

Designer / Date: David Mitchell, 2012.

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

Modules / Paper shape / Folding geometry: 30 modules folded from squares using standard folding geometry.

Designer / Date: David Mitchell, 1989.

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4.
 
  Name: Apollo 20 or just Apollo - a pierced decorative dodecahedron.

Modules / Paper shape / Folding geometry: 20 modules from hexagons or double bronze rectangles using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 1992.

Diagrams: Not yet available.
 
  Name: The Banded 8-point Star - an 8-point Stubby Star surrounded by under and overlapping bands of colour which are integral to the structural modules

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 Banded 20-point Star, or just the Banded Star - a 20-point Stubby Star surrounded by under and overlapping bands of colour which are integral to the structural modules.

Modules / Paper shape / Folding geometry: 30 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: Ariadne 30, or just, Ariadne - a 20-point Stubby Star to which the metamorphosis 1 distortion has been applied.

Modules / Paper shape / Folding geometry: 30 modules folded from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990.

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

Modules / Paper shape / Folding geometry: 6 modules from silver rectangles .

Designer / Date: David Mitchell, 1990.

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

Modules / Paper shape / Folding geometry: 2 modules from squares using various folding geometries.

Designer / Date: David Mitchell, 1988.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Binary 2

Modules / Paper shape / Folding geometry: 2 modules from stars of David using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 2008.

Diagrams: Not yet available.
 
  Name: Celestial (version 3)

Modules / Paper shape / Folding geometry: From 60 Semi-Sonobe modules folded from 2x1 rectangles using standard folding geometry.

Designer / Date: David Mitchell, 2013.

Diagrams: Not yet available.
 
  Name: Cloud of Stars (version 1) - a version of Hachiro Kamata's Star Decorative Ball in which the modular method allows each star to be coloured independently.

Modules / Paper shape / Folding geometry: From 30 compound modules each made up of 1 module folded from a 2x1 rectangle and 2 modules folded from squares, all using standard folding geometry.

Designer / Date: David Mitchell, 1999.

Diagrams: In the first edition of Paper Crystals - Water Trade - ISBN 0-9534774-2-8.
 
  Name: Cloud of Stars ( version 2)

Modules / Paper shape / Folding geometry: Made by adding 60 cladding pieces to an underlying Star Decorative Ball made from 30 Sonobe-type modules. All modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2007.

Diagrams: Not yet available.
 
  Name: Cloud of Stars (version 3)

Modules / Paper shape / Folding geometry: From 60 Semi-Sonobe modules folded from 2x1 rectangles using standard folding geometry.

Designer / Date: David Mitchell, 2013.

Diagrams: Not yet available.
 
  Name: Curvaceous

Modules / Paper shape / Folding geometry: Made from 6 modules folded from squares using standard folding geometry and 12 folded from silver rectangles.

Designer / Date: David Mitchell, 1998.

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

 
  Name: Cushions are a series of 2-part designs from squares and other rectangles developed from Molly Kahn's Preliminary Ornament and the Oblong Ornament.

Modules / Paper shape / Folding geometry: 2 modules from any rectangle.

Designer / Date: In 2004, soon after seeing Paulo Mulatinho's UFO, I realised the same idea could be applied to larger grids and other rectangles. In 2005 Tung Ken Lam realised that the divisions of the grids need not be uniform.

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

Modules / Paper shape / Folding geometry: 6 modules from silver rectangles.

Designer / Date: David Mitchell, 2002.

Diagrams: Not yet available.
 
  Name: Decorative Rhombic Dodecahedron

Modules / Paper shape / Folding geometry: Made by adding a 6-part cladding to David Brill's Skeletal (or Nolid) Cube, which is itself made from 12 modules. All modules from silver rectangles.

Designer / Date: David Mitchell, 1992.

Diagrams: In Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X

 
  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: Electra 30 or just Electra - a pierced decorative icosidodecahedron.

Modules / Paper shape / Folding geometry: 30 modules folded from squares using mock platinum folding geometry.

Designer / Date: David Mitchell, 1989.

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4 // On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Electra 60 - a pierced decorative rhombicosidodecahedron

Modules / Paper shape / Folding geometry: 60 modules folded from squares using mock platinum folding geometry.

Designer / Date: David Mitchell, 1989.

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4 // On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Elite

Modules / Paper shape / Folding geometry: 24 modules from silver rectangles.

Designer / Date: David Mitchell, 1991.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Elite 2

Modules / Paper shape / Folding geometry: 24 modules from silver rectangles applied as a cladding to ZYX. ZYX is made from 12 modules folded from silver rectangles using standard folding geometry.

Designer / Date: David Mitchell, 1993.

Diagrams: Not yet available.
 
  Name: Enigma Cube (2-part)

Modules / Paper shape / Folding geometry: 2 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1988.

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

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry. Each module is in the form of a nolid octahedron. The modules are gently twisted together inside the form to hold each other in place.

Designer / Date: David Mitchell, 2003.

Diagrams: Not yet available.
 
  Name: Four Cubes

Modules / Paper shape / Folding geometry: 6 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: Gaia

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

Designer / Date: David Mitchell, 1989.

Diagrams: In Paper Crystals - David Mitchell - Water Trade - ISBN 9780953477494.
 
  Name: Gemini 30 or just Gemini - a decorative icosidodecahedron.

Modules / Paper shape / Folding geometry: 30 modules folded from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990.

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4.
 
  Name: Gemini 60 - a decorative rhombicosidodecahedron.

Modules / Paper shape / Folding geometry: 60 modules folded from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990.

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

Modules / Paper shape / Folding geometry: Made by adding 30 embellishments in the form of tear-shaped tubes to a 30 module Matrix base. All modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2015.

Diagrams: Not yet available.
 
  Name: Odditty

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

Designer / Date: David Mitchell, 1998.

Diagrams: Not yet available.
 
  Name: Odyssey

Modules / Paper shape / Folding geometry: Made by adding 30 strengtheners to a 30 module Cube-Corner Dodecahedron. Strengtheners from silver rectangles, other modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2015.

Diagrams: 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: Omicron

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry. Designs of many different proportions are possible.

Designer / Date: David Mitchell, 1990.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Phaedra30 or just Phaedra - a decorative variation of Ariadne.

Modules / Paper shape / Folding geometry: 30 modules folded from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990.

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Proteus 30, or just Proteus - a decorative pierced icosidodecahedron

Modules / Paper shape / Folding geometry: 30 modules folded 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: The Rosebud Octahedron - created by applying the rosebud distortion to one dimple of Robert Neale's Octahedron. Up to 4 of the 8 dimples can be distorted in this way.

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

Designer / Date: David Mitchell, 1999.

Diagrams: In Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0.
 
  Name: The Rosebud Octahedron (Fully Distorted)

Modules / Paper shape / Folding geometry: 8 modules folded from 3x1 rectangles using standard folding geometry. A module that will achieve a similar result can be folded from a 2x1 rectangle but the final result is less successful.

Designer / Date: David Mitchell, 2014.

Diagrams: Not yet available.
 
  Name: Rosebud Icosahedron

Modules / Paper shape / Folding geometry: 30 modules folded from squares using standard folding geometry.

Designer / Date: David Mitchell, 2014.

Diagrams: Not yet available.
 
  Name: The Semi-Star

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

Designer / Date: David Mitchell, 1988.

Diagrams: In Paper Crystals - David Mitchell - Water Trade - ISBN 9780953477494.
 
  Name: Six Intersecting Rhombic Tetrahedra

Modules / Paper shape / Folding geometry: 36 modules of two different kinds, all folded from silver rectangles, 12 tubes and 24 joining pieces.

Designer / Date: David Mitchell, 1999.

Diagrams: Not yet available.
 
  Name: Spiral Cluster 120

Modules / Paper shape / Folding geometry: From 30 compound modules, each of which is made from 4 modules folded from squares of paper using standard folding geometry.

Designer / Date: David Mitchell, 1999.

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4
 
  Name: Star Contrast Ball

Modules / Paper shape / Folding geometry: 30 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1991.

Diagrams: Not yet available.
 
  Name: Stella Nova 30 or just Stella Nova

Modules / Paper shape / Folding geometry: 30 modules folded from a custom rectangle using 60/30 degree folding geometry, although they can also be folded from 4x1 rectangles with only a small loss of elegance.

Designer / Date: David Mitchell, 2008.

Diagrams: Not yet available.
 
  Name: Stella Nova Duo 30 or just Stella Nova Duo

Modules / Paper shape / Folding geometry: 30 modules folded from a custom rectangle using 60/30 degree folding geometry, although they can also be folded from 4x1 rectangles with only a small loss of elegance.

Designer / Date: David Mitchell, 2008.

Diagrams: Not yet available.
 
  Name: Thingamy

Modules / Paper shape / Folding geometry: 2 modules from silver rectangles.

Designer / Date: David Mitchell, 1990.

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

Modules / Paper shape / Folding geometry: 6 modules from squares using standard folding geometry. Three separate methods of folding a suitable module are known.

Designer / Date: David Mitchell, 1992.

Diagrams: Not yet available.
 
  Name: Vulcan 30 or just Vulcan - a decorative pierced icosahedron.

Modules / Paper shape / Folding geometry: 30 modules folded from a custom rectangle using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 2008.

Diagrams: Not yet available.
 
  Name: Waterbomb Star

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

Designer / Date: David Mitchell, 1988.

Diagrams: Not yet available.
 
  Name: Zigzag 30 or just Zigzag - a simplification of Sappho.

Modules / Paper shape / Folding geometry: 30 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2012.

Diagrams: In Paper Crystals (2nd Edition) - Water Trade - ISBN 978-0-9534774-9-4.
 
  Name: Zigzag 36

Modules / Paper shape / Folding geometry: 36 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2012.

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