Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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Multipurpose Modules
 

Multipurpose modules are modules whose configuration can be varied so that they will go together to make a number of different modular forms. New design work in this area may involve the discovery / design of original multipurpose modules, deriving new developments or variations from existing ones or combining existing modules, new modules and new derivations in original ways.
 
Developments of the Sonobe Module
 

The Sonobe module was the original multipurpose module. It was used by its inventor, Mitsonobu Sonobe, to make, first the 6-part Cube, then the 12-part Cube and the 12-part 8-point Stubby Star, the modules for each of these forms being configured in different ways. Both the latter configurations included a diagonal crease across the central square area of the module at right angles to the slit. We can call such modules the Alpha version of the design.

It is also possible to fold a Beta version of the module, in which the diagonal crease across the central square area runs in the alternate direction, ie along the line of the slit rather than across it. A basic Beta Sonobe module can be found in Origami for the Connoisseur by Kunihiko Kasahara and Toshie Takahama, which was first published in 1985.

Mirror-image versions of both the Alpha and Beta forms of the module are possible. Mirror-image forms often occur accidentally when trying to fold large numbers of modules.

The corner-pocket version of the design, where two opposite corners are inverted to create pockets, was originated by Tomoko Fuse in the mid 1980s.

Kunihiko Kasahara originated another version of the Sonobe module, which he called the Simple Sonobe module, in which two opposite corners of the module are simply folded backwards (nstead of being folded forwards and tucked in or inverted).

One of my own contributions, I believe, has been the development of the Triangle Sonobe module where two adjacent (rather than opposite) corners are folded inwards, inverted or folded behind. Triangle Sonobes are not, however, anywhere near as versatile as the Alpha or Beta versions.

Another of my contributions has been the realisation that different versions of the Sonobe module can be combined within the same design to create Motley Sonobe designs.

Here are some of my other developments of this versatile module:
 
  Name: The Sonobe Silveroctahedron, which in its most basic form, as pictured here, can be made by combining two Alpha Sonobe modules with two Beta Sonobe modules. This form will also collapse and pop-up back into shape.

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

Designer / Date: David Mitchell, 1989

Reference:

Diagrams: On-line diagrams are available on the Modular Designs page of this site as part of the diagrams for my Ariadne modular sculpture.
 
  Name: Ariadne modules (Corner-pocket Sonobe modules to which the metamorphosis 1 distortion has been applied) - Decorative development of the Sonobe module which will make the same forms as the original.

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

Designer / Date: David Mitchell, 1990

Reference: 064

Diagrams: On-line diagrams are available on the Modular Designs page of this site as part of the diagrams for my Ariadne modular sculpture.
 
    Name: Minos modules (Corner-pocket Sonobe modules to which the metamorphosis 2 distortion has been applied) - Decorative development of the Sonobe module which will make the same forms as the original.

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

Designer / Date: David Mitchell, 1990

Reference: 064

Diagrams: Not yet available.
 
  Name: Assymetric Sonobe, Corner-Pocket Sonobe and Simple Sonobe modules. These are a development of the Sonobe module that will go together to create unusually assymetrically patterned cubes, cube combinations and silverhedra. The proportions of the two assymetric elements of the module can be varied. I also call the corner-pocket version Mondrian modules. When Mondrian modules of different proportions are combined in the same design I call them Cockeyed designs.

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

Forms: 12 identical modules will go together to make a Mondrian Cube, and 24, in two ways, to make a Mondrian 8-point Stubby Star. It is not possible to make a 20-point Stubby Star from assymetric modules. The same forms can be made in Cockeyed versions by combining sets of modules of differing proportions.

Designer / Date: David Mitchell, 1995

Reference: 119

Diagrams: Synergy 3 - Water Trade // Diagrams for one version of the module and the Mondrian Cube are available on the Modular Designs page of this site.
 
  Name: Semi-Sonobe modules. These modules will make all the same forms as the original Sonobe module. They are most easily made by the simple expedient of cutting a Sonobe module in half.

Modules / Paper shape / Folding geometry: From 2x1 rectangles using standard folding geometry.

Designer / Date: David Mitchell, 2013

Reference: 354

Diagrams: Not yet available.
 
Developments of Nick Robinson's Rhombic Module
 
Nick Robinson's Rhombic Module is a version of the Corner-Pocket Sonobe module folded from a sheet of A4 paper rather than from a square. In fact the design of the module will work from any oblong.

Here are some of my developments of this design:
 
  Name: Equilateral Modules - a development of Nick Robinson's Rhombic Module. These modules will combine in basic and mirror-image forms to make many robust deltahedra. A delta version is also possible.

Modules / Paper shape / Folding geometry: From bronze rectangles using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 1998

Reference: 162

Diagrams: In Mathematical Origami (2nd Edition) - David Mitchell - Tarquin publications - ISBN 9781911093169
 
  Name: Rhombic Triangle modules - a triangular version of Nick Robinson's Rhombic module. These modules will combine to make several rhombic solids. A four-pockets module is also possible. Variants with other arrangements of flaps and pockets are only possible if the paper is cut.

Modules / Paper shape / Folding geometry: From silver rectangles using silver rectangle folding geometry.

Designer / Date: David Mitchell, 2004

Reference: 267

Diagrams: In Mathematical Origami (2nd Edition) - David Mitchell - Tarquin publications - ISBN 9781911093169
 
Letterbox Modules
 
    Name: Simple Letterbox modules. All versions will go together to create cubes, cube combinations and silverhedra. Alpha, Beta, mirror-image and triangular versions are possible.

Modules / Paper shape / Folding geometry: From 3x2 rectangles using standard folding geometry.

Designer / Date: David Mitchell, 1987.

Reference: 048

Diagrams: Alpha modules - Synergy 2 - Water Trade // On-line diagrams are available on the Modular Designs page of this site.
 
    Name: Assymetric Simple Letterbox modules.

Modules / Paper shape / Folding geometry: From 3x2 rectangles using standard folding geometry.

Designer / Date: David Mitchell, 1995.

Reference: 119

Diagrams: Not yet available.
 
    Name: Basic Letterbox modules

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

Designer / Date: David Mitchell, 1987.

Reference: 048

Diagrams:
 
    Name: Assymetric Basic Letterbox modules

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

Designer / Date: David Mitchell, 1995.

Reference: 119

Diagrams: Not yet available.
 
    Name: Contrast Pattern Letterbox modules - many patterned variations.

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

Designer / Date: David Mitchell, 1989.

Reference: 048

Diagrams: Alpha modules - Synergy 2 - Water Trade // On-line diagrams are available on the Modular Designs page of this site.
 
Other Original Multipurpose Modules
 
  Name: Banded modules. Various symmetric, assymetric and doubly assymetric designs, all of which have a coloured band in the centre and pockets on either side beneath the band. Will go together to make a variety of banded cubes and silverhedra where the various differently coloured bands appear to run right around the design.

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

Designer / Date: David Mitchell, 2001

Reference: 226

Diagrams: On-line diagrams for one version of the module are available on the Modular Designs page of this site.
 
  Name: Darwin modules. The basic module has four white flaps which can be used to create many patterned variant modules including the well known Cyclone module. The modules will go together to make a wide variety of decorative cubes and silverhedra. Modules of different patterns can easily be combined within the same modular form.

Modules / Paper shape / Folding geometry: From squares using standard folding geometry / based on division into thirds..

Designer / Date: David Mitchell, 2001

Reference: 231

Diagrams: Synergy 2 - Water Trade // On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Intersection modules. Will go together to make many inverted edge open frame designs.

Modules / Paper shape / Folding geometry: From squares / other rectangles using standard folding geometry.

Designer / Date: David Mitchell, 2003

Reference: 256

Diagrams: Diagrams not yet available.
 
  Name: Matrix modules. Will go together to make inverted edge open frame designs.

Modules / Paper shape / Folding geometry: From squares using 60/30 degree folding geometry.

Designer / Date: David Mitchell, 2015

Reference: 372

Diagrams: Diagrams not yet available.
 
  Name: Maverick modules. Two mirror-image modules will go together to form a Marriage of Opposites. Maverick modules will also combine with Sonobe and Letterbox modules to create Motley forms.

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

Designer / Date: David Mitchell, 1990

Reference:063

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Reptile modules. Will go togeter to create patterned deltahedra.

Modules / Paper shape / Folding geometry: From square using 60/30 degree geometry.

Designer / Date: David Mitchell, 1997

Reference: 146

Diagrams: First published in BOM 189 of April 1998 // On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Simplex modules. These modules will combine to make any solid shape whose faces are squares or silver triangles.

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

Designer / Date: David Mitchell, 1988.

Reference: 035

Diagrams: On-line diagrams are available on the Modular Designs page of this site.
 
  Name: Simplified Skillman modules. Combine to make pierced designs based on a large variety of polyhedral forms.

Modules / Paper shape / Folding geometry: From bronze rectangles using 60/30 folding geometry.

Designer / Date: David Mitchell, 2003.

Reference: 258

Diagrams: Diagrams not yet available
 
  Name: Stella Nova modules. Combine to make multi-colour stars based on deltahedra..

Modules / Paper shape / Folding geometry: From 4x1 rectangles using 60/30 degree geometry.

Designer / Date: David Mitchell, 2008

Reference: 322

Diagrams: Not yet available.
 
  Name: Vulcan modules. Combine to make pierced stars based on a large variety of polyhedral forms.

Modules / Paper shape / Folding geometry: From custom sized rectangles using 60/30 folding geometry.

Designer / Date: David Mitchell, 2008.

Reference:323

Diagrams: Diagrams not yet available // Photo of Vulcan icosahedron in Le Pli 113-114 - Mai 2009