Rona Gurkewitz' Modular Origami Polyhedra Systems Page

Rona Gurkewitz
Associate Professor of Math and Computer Science
Math and Computer Science Department
Western Connecticut State University
Danbury, Ct 06810
Phone: (203) 837-9354
gurkewitzr@wcsu.edu

At right: "Christmas Wreath" by Bennett Arnstein made from 10 interlocking truncated octahedra, each made from 24 "one piece triangle modules" from our book "3D Geometric Origami: Modular Polyhedra", Gurkewitz and Arnstein Dover 96
This site is about modular origami polyhedra, especially what we define as Modular Origami Polyhedra Systems, and photos of models from my books "3D Geometric Origami:Modular Polyhedra",Gurkewitz and Arnstein, Dover 96 and "Modular Origami Polyhedra"Simon,Arnstein and Gurkewitz, Dover 99 which emphasize these systems.
Origami models were folded by Bennett Arnstein and Rona Gurkewitz.
last modified 10-9-00

Contents

• Rona Gurkewitz' Definition of Modular Origami Polyhedra Systems
• Gallery of Some Modular Origami Polyhedra Models from Rona Gurkewitz, Bennett Arnstein and Lewis Simon's books
• Rona Gurkewitz' other Origami Work and links
• Links to other Origami and Polyhedra Sites
• Diagrams for a math lesson Laura Kruskal's 'Rectangle to a Square Pass a Note'
• More diagrams(under construction)

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Rona Gurkewitz' Definition of Modular Origami Polyhedra Systems

Definition

References

• Books
• Other origami and polyhedra sites(under construction)

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Books

• "3-D Geometric Origami: Modular Polyhedra",Gurkewitz, Arnstein Dover 96
  
• "Modular Origami Polyhedra", Simon, Arnstein, Gurkewitz Dover 99
  

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Gallery of Selected Models(more photos to come)

• Some models from 'Modular Origami Polyhedra', Simon, Arnstein, Gurkewitz 99

  photographs by Bill Quinnell
  Mouseover a photo to see a larger image, a caption and credits
  
  
  Decoration Box by Lewis Simon with adaptations
  by Arnstein and Gurkewitz
  12 modules from U.S. dollar bills
  
  
  
  Cubes from Variations of Decoration Box
  by Lewis Simon and Bennett Arnstein
  12 modules per cube
  
  
  
  
  Decoration Box Variations, 12 modules
  Sonobe Variation Cubes, 12 and 24 modules
  each module is two pieces of paper back to back
  
  
  
  Decoration Box System Dodecahedron,
  Lewis Simon (and independently Bob Neale)
  30 modules(edge modules)
  Triangular Gyroscope System Dodecahedron
  Lewis Simon, Bennett Arnstein
  20 modules(vertex modules)
  
  
  
  Decoration Box System,
  variations in number
  of modules and angles on modules
  original module by Lewis Simon
  60 degree angle module is by Jim Plank
  45 degree angle is by Bennett Arnstein
  90 degree angle is by Lewis Simon
  Octahedron,12 modules
  Cuboctahedron,24 modules
  Cube, 12 modules
  
  
  
  
  Decoration Box System
  by Lewis Simon
  Stellated Icosahedron, 60 modules, each module has
  90 angle on one end and 45 degree angle on the other end
  Tetrahedron,6 modules, each module has 60 angle on both ends
  Icosahedron,30 modules, each module has 60 angle on both ends
  
  
  
  

Sonobe System model
Stellated icosahedron, 30 basic Sonobe modules

Sonobe System models
Stellated icosahedron, 30 modules
Cube, 6 modules
Hexahedron, 3 modules
Stellated octahedron, 12 modules

Decoration Box Module made into
a Sonobe Shape Stellated Icosahedron
by Bennett Arnstein,60 modules, each module has 45 angle at one end and
90 angle at the other

Ninja Star variation of
Decoration Box Module made into Sonobe shapes
by Lewis Simon
Stellated Icosahedron, 60 modules with 90 angle at one end, 45 angle at other
Cube, 12 modules with 90 angle at each end

Square Gyroscope, Lewis Simon, 6
modules from squares"

Sunkated' square gyroscope
module
by Rona Gurkewitz
Rhombicosidodecahedron, 60 modules
Icosidodecahedron, 30 modules
Octahedron, 6 modules

• Some models from '3D Geometric Origami:Modular Polyhedra', Gurkewitz,Arnstein; Dover 96

  photographs by Bill Quinnell
  Mouseover a photo to see a larger image, a caption and credits
  
  Truncated Icosahedron or "Buckyball"
  60 one piece triangle(one piece triangular
  gyroscope) modules
  Arnstein
  
  
  The Egg', truncated hexadecahedron
  (16 triangle deltahedron), 48 one piece triangle
  (one piece triangular gyroscope) modules
  Arnstein, Gurkewitz"
  
  
  
  Great Dodecahedron
  12 Simplified pentagon modules
  Modules are pentagon analogue of
  one piece triangle modules
  Arnstein"
  
  
  
  Icosahedron
  30 triangle edge modules
  Lewis Simon"
  
  
  
  Octahedron
  12 triangle edge modules
  Lewis Simon" "
  
  
  
  Dodecahedron Flower Ball
  20 triangular spike ball modules
  Gurkewitz, Arnstein
  
  
  
  
  

Super Spike Ball
Based on rhombicuboctahedron from
24 spike ball modules
Gurkewitz

Equilateral stellation of icosahedron
30 chain of 4 equilateral triangle modules
Simon, Arnstein

Stellation of the icosahedron
with 30, 36 degree isosceles triangle modules, view 1
Arnstein

Stellation of the icosahedron
with 30, 36 degree isosceles triangle modules, view 2
Arnstein

Stellation of the icosahedron
with 30, 45 degree isosceles triangle modules, view 1
Gurkewitz"

Stellation of the icosahedron
with 30, 45 degree isosceles triangle modules, view 2
Gurkewitz"

• Miscellaneous Models

  Mouseover the photo for a larger image
  

Slinky by Gay Merrill Gross
Adapted to dollar bills by
Rona Gurkewitz"

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