Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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Macromodular Sculptures
 
Macromodular sculptures are second generation modular designs built by combining complete modular assemblies into larger structures either with, or without, the use of joining or separating pieces.

My macromodular sculptures are intended to be 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.

Many of these designs are explained in my book Building with Butterflies.

Larger pictures of many of these designs can be found in the Gallery of Macromodular Sculpture.

All of the designs on this page are abstract / geometrical except the Macromodular Fox which is abstract / representational.

 
Towers
 
  Name: The Abstract Fox - a fox made using a Twin Open Equilateral Triangular Prism for a body and Paul Jackson's Cube for a head.

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

Designer / Date: David Mitchell, 2020.

Reference: 573

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

 
  Name: The Columbus Tower, also known as the Columbus Cubes or Tower of Columbus Cubes, is made by the simple expedient of stacking Columbus Cubes one on top of the other. Columbus Towers can be combined to form walls and forests.

Modules / Paper shape / Folding geometry: Each Columbus Cube is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1989.

Reference: 043

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3 // Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0 // On-line diagrams are available on the Macromodular Designs page of this site.

 
  Name: The Tower of Columbus Cuboids is made by stacking Columbus Cuboids one on top of the other. Towers of Columbus Cuboids can be combined to form walls and forests.

Modules / Paper shape / Folding geometry: Each Columbus Cuboid is made from 6 modules folded from A4 or US Letter size sheets of paper using standard folding geometry.

Designer / Date: David Mitchell, 2015.

Reference: 374

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

 
  Name: The Crooked Tower is made by combining Paul Jackson Cubes and Robert Neale Octahedra alternately in a stack

Modules / Paper shape / Folding geometry: Each Paul Jackson Cube is made from 6 modules from squares using standard folding geometry. Each Robert Neale Octahedron is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1997.

Reference: 138

Diagrams: Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: Digitalis - a macromodular sculpture made by stacking Abstract Foxes.

Modules / Paper shape / Folding geometry: All modules from square paper using standard folding geometry.

Designer / Date: David Mitchell, 2020.

Reference: 573

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

 
  Name: Helterskelter - a macromodular sculpture made by stacking Gamma Antiprisms.

Modules / Paper shape / Folding geometry: Each Gamma Antiprism is made from 8 squares using standard folding geometry.

Designer / Date: David Mitchell, 1999.

Reference: 179

Diagrams: Photo only in Citizen K International magazine Spring 99 // Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0.

 
  Name: The Icarus Tower - a macromodular sculpture built from Icarus Cubes using joining pieces.

Modules / Paper shape / Folding geometry: Each Icarus Cube is made from 6 modules from squares using standard folding geometry. Each joining piece is folded from a one sixteenth size square using standard folding geometry.

Designer / Date: David Mitchell, 1998.

Reference: 161

Diagrams: Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: The Leaning Tower - a macromodular design made by combining Paul Jackson Cubes and Tricornes in a stack

Modules / Paper shape / Folding geometry: Each Paul Jackson Cube is made from 6 modules from squares using standard folding geometry. Each Tricorne is made from 3 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1998.

Reference: 167

Diagrams: Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: The Octahedral Tower - a macromodular design made by stacking Robert Neale Octahedra with the aid of joining pieces.

Modules / Paper shape / Folding geometry: Each Robert Neale Octahedron is made from 6 modules from squares using standard folding geometry. Each joining piece is made from a square using standard folding geometry.

Designer / Date: David Mitchell, 1998.

Reference: 164

Diagrams: Building with Butterflies - Water Trade - ISBN 0-9534774-1-X (as Tower of Octahedra) // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: Treesnake - a macromodular design built from Diamond Prisms.

Modules / Paper shape / Folding geometry: Each Diamond Prism is made from 8 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1998.

Reference: 155

Diagrams: Photo only in Citizen K International magazine Spring 99 // Building with Butterflies - Water Trade - ISBN 0-9534774-1-X

 
  Name: Tower of Whatnots - tower built from Whatnot macromodules

Modules / Paper shape / Folding geometry: Eavh Whatnot is made from 2 modules from double bronze rectangles using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 2016.

Reference: 582

Diagrams: Not yet available.

 
Pyramids and Tetrahedra
 
  Name: 4 Regular Tetrahedra and a Regular Octahedron combined to make a larger Regular Tetrahedron.

Modules / Paper shape / Folding geometry:

Designer / Date: David Mitchell, 1997.

Reference:

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3

 
  Name: 4 Rhombic Pyramids combined to make a Rhombic Tetrahedron

Modules / Paper shape / Folding geometry:

Designer / Date: David Mitchell, 1997.

Reference: 147

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3

 
  Name: 8 Rhombic Pyramids into a larger Rhombic Pyramid

Modules / Paper shape / Folding geometry: Rhombic Pyramids are made from modules folded from silver rectangles.

Designer / Date: David Mitchell, 2000

Reference: 147

Diagrams: In Mathematical Origami (2nd Edition) - David Mitchell - Tarquin publications - ISBN 9781911093169

 
  Name: 8 Rhombic Tetrahedra into a larger Rhombic Tetrahedron.

Modules / Paper shape / Folding geometry: Rhombic Tetrahedra are made from modules folded from silver rectangles.

Designer / Date: David Mitchell, 1996

Reference: 129

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3

 
  Name: Aleph Pyramids - macromodular sculptures built from Aleph Prisms.

Modules / Paper shape / Folding geometry: Each Aleph Prism is made from 3 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2005.

Reference: 270

Diagrams: Diagrams not yet available.

 
  Name: Alpha Pyramids - macromodular sculptures built from Alpha Prisms using joining pieces.

Modules / Paper shape / Folding geometry: Each Alpha Prism is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1997.

Reference: 135

Diagrams: Photo only in Citizen K International magazine Spring 99 // Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: Columbus Cubes can be combined with separating pieces to produce the Columbus Pyramid shown here.

Modules / Paper shape / Folding geometry: Each Columbus Cube is made from 6 modules from squares using standard folding geometry. Each joining piece is from a square using standard folding geometry.

Designer / Date: David Mitchell, 1997.

Reference: 137

Diagrams: Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: Damocles - a macromodular design made by combining Alpha and Beta Prisms.

Modules / Paper shape / Folding geometry: Each Alpha Prism and each Beta Prism is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1997.

Reference: 136

Diagrams: First published without the orange inserts as Tower of Babel in Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // As Damocles with inserts in Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0.

 
  Name: Elite Pyramid - Macromodular design made from Elites stacked using joining pieces.

Modules / Paper shape / Folding geometry: Each Alpha Prism and each Beta Prism is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1991.

Reference: 076

Diagrams: Building with Butterflies (1st Edition) - Water Trade - ISBN 0-9534774-1-X

 
  Name: Four Octahedra - four Robert Neale Octahedra linked with joining pieces from squares in such a way that it appears to be made of six intersecting planes. Designs with more linked ocahedra are possible.

Modules / Paper shape / Folding geometry: Each Robert Neale Octahedron is made from 6 modules from squares using standard folding geometry. Each joining piece is from a square using standard folding geometry.

Designer / Date: David Mitchell, 2016. Update of work from 1995.

Reference: 164

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

 
  Name: Mothership - design made using Paulo Mulatinho's UFO as a macro-module - from squares.

Modules / Paper shape / Folding geometry: Each UFO is made from 2 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2001.

Reference: 265

Diagrams: Not yet avaiable.

 
  Name: The Octahedral Pyramid - single colour version - a macronodular design made using Robert Neale Octaahedra as macromodules and linked by joining pieces.

Modules / Paper shape / Folding geometry: Each Robert Neale Octahedron is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1998.

Reference: 164

Diagrams: Building with Butterflies - Water Trade - ISBN 0-9534774-1-X // Material and Immaterial: Paper Art in Israel - Exhibition Catalogue - 2008 // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: The Octacube Pyramid - made by combining Paul Jackson Cubes and Robert Neale Octahedra.

Modules / Paper shape / Folding geometry: Each Paul Jackson Cube is made from 6 modules from squares using standard folding geometry. Each Robert Neale Octahedron is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1997.

Reference:

Diagrams: Not yet available.

 
  Name: Slide - made by combining Columbus Cubes, Paul Jackson Cubes and truncated hexahedra macromodules in a pyramidal form. The cubes and truncated hexahedra are linked together with joining pieces.

Modules / Paper shape / Folding geometry: Each Paul Jackson Cube and each Columbus Cube is made from 6 modules from squares using standard folding geometry. Each truncated hexahedron is made from 3 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 2010.

Reference: 167

Diagrams: Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0. These diagrams incorrectly show to use Tricorne macromodules rather than Mark Two macromodules / Corrected diagrams are now available on the Macromodular Designs page of this site.

 
  Name: Temple of the Winds - a macromodular design made from triangular prisms and joining/supporting pieces.

Modules / Paper shape / Folding geometry: Each prism is made from 2 squares using standard folding geometry. Each joining piece is made from a square using standard folding geometry.

Designer / Date: David Mitchell, 2014.

Reference: 370

Diagrams: Not yet available.

 
    Name: Three-quarter Cube Sierpinski Pyramid

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

Designer / Date: Macromodules David Mitchell, 2016. Sierpinski Pyramid concept by Kumars Sharif.

Reference: 373

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

 
Rings
 
  Name: Ring of Cubes. The unmathematical geometry of the design was analysed in passing by Jeannine Mosely in an article in Origami3 - A K Peters Ltd - ISBN 1568811810 entitled 'The Validity of the Orb, An Origami Model'. A drawing of the design features on the cover artwork.

Version 1: made by glueing five Columbus Cubes together

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

Designer / Date: David Mitchell, 1990 (both versions).

Reference: 043

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3

Version 2: made by linking together five Ring of Cubes macromodules, which are provided with the necessary tabs and pockets to make this possible without needing to use glue.

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

Reference: 057

Diagrams: Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: Ring of Elite 1s - 5 Elite 1s linked by joining pieces. A ball of 20 Elite 1s is also possible.

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

Designer / Date: David Mitchell, 1993.

Reference: 067

Diagrams: Not yet available.

 
  Name: Ring of Elite 2s - 5 Elite 2s linked by joining pieces. A ball of 20 Elite 2s is also possible.

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

Designer / Date: David Mitchell, 1993.

Reference: 067

Diagrams: Not yet available.

 
  Name: Stargate - 5 Artifacts linked by joining pieces.

Modules / Paper shape / Folding geometry: All modules from silver rectangles using silver rectangle folding geometry.

Designer / Date: David Mitchell, 1995.

Reference: 056

Diagrams: In Complete Origami - Collins and Brown - David Mitchell - ISBN 978-1-84340-397-5 // On-line diagrams are available on the Diagrams: On-line diagrams are available on the Macromodular Designs page of this site.

 
Balls
 
  Name: Ball of Cubes. 20 cubes arranged at the vertices of a dodecahedron. Further macromodules can be added to produce more complex forms.

Version 1: Glued

Modules / Paper shape / Folding geometry: 120 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990

Reference: 043

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3 // Discussed in Compound Platonic Polyhedra in Origami - Lengvarszky, Zsolt - Mathematics Magazine - Volume 79, Number 3, June 2006 , pp. 190-198(9)

Version 2: Pure origami

Modules / Paper shape / Folding geometry: 120 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1990

Reference: 057

Diagrams: BOM 146 February 1991 // Building with Butterflies (2nd Edition) - Water Trade - ISBN 978-9534774-7-0

 
  Name: Nexus - 20 Artifacts linked by joining pieces.

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

Designer / Date: David Mitchell, 1995.

Reference: 056

Diagrams: // May 22nd photo in Origami 2006 Calendar - Andrews McMeel - ISBN 0-7407-5195-6 // On-line diagrams are available on the Modular and Macromodular Designs page of this site.

 
Lattices
 
  Name: The Octacube is made by combining eight Paul Jackson Cubes and six Robert Neale Octahedra. Larger versions can be constructed by adding more macromodules.

Modules / Paper shape / Folding geometry: Each Paul Jackson Cube is made from 6 modules from squares using standard folding geometry. Each Robert Neale Octahedron is made from 6 modules from squares using standard folding geometry.

Designer / Date: David Mitchell, 1997.

Reference:

Diagrams: Not yet available.

 
  Name: Borromean Lattice - lattice made by combining Borromean Links designs using simple joining pieces.

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

Designer / Date: David Mitchell, 1999.

Reference: 058

Diagrams: Not yet available.

 
  Name: The Elite Hypercube - made by combining 20 Elite 1 macromodules using joining pieces. In theory it would also be possible to build this structure using Elite 2 macromodules.

Modules / Paper shape / Folding geometry: All modules and joining pieces folded from silver rectangles.

Designer / Date: David Mitchell, 1991.

Reference: 076

Diagrams: Building with Butterflies (1st Edition) - Water Trade - ISBN 0-9534774-1-X // On-line diagrams are available on the Diagrams: On-line diagrams are available on the Macromodular Designs page of this site.