## Rona Gurkewitz' Modular Origami Polyhedra Systems Page

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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

### Definition

In the book "3-D Geometric Origami: Modular Polyhedra", Gurkewitz and Arnstein 96, a "system" of origami polyhedra models is defined as a collection of models that can be folded from different numbers of a given module or from modules that have related folding sequences. Another possibility is to vary the starting polygonal shape of the paper used for a module. A third possibility is to systematically vary an angle or angles on a modules to produce a new module that makes a different polyhedron. In the Gallery see if you can visually tell which models belong to the same system. You can check by reading the descriptions.Email me for help or with questions.

### References

## Books

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

- "Modular Origami Polyhedra", Simon, Arnstein, Gurkewitz Dover 99

Email me for help or with questions. gurkewitzr@wcsu.edu

## 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"

This page transfered to http://www.make-origami.com/RonaGurkewitz/home.php in May, 2017 with permission from Rona Gurkewitz.

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