Rona Gurkewitz - Beginners Book of Modular Origami Polyhedra: The Platonic Solids
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- Book:Beginners Book of Modular Origami Polyhedra: The Platonic Solids
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Beginners Book of Modular Origami Polyhedra: The Platonic Solids: summary, description and annotation
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Whether or not youre familiar with traditional origami models, youre sure to be captivated by the fun and fascination of creating abstract geometric forms. This book by an expert paperfolder offers a clear, concise introduction to the special techniques for making beautiful, complex polyhedra models.
These 17 projects are based on the classic Platonic solids: the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Folders at every level of experience, from absolute beginners to old hands, will appreciate the step-by-step diagrams and their detailed views of the models assembly. Additional helpful features include photos of the complete models, background on the Platonic solids, and references.
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Modular origami is origami made from several sheets of paper that have been folded into modules, also called units. The modules are usually identically folded but may be of several types. The modules are assembled into models that most often are patterned after the 3D geometric shapes called polyhedra.
Underlying most 3D modular origami is a uniform, convex polyhedral shape. The modules in the model are in positions corresponding to either the faces, edges or corners (vertices) of the polyhedral shape. Convex polyhedra dont have spikes. Uniform polyhedra have all of their corners having the same arrangement of shapes around them. For example, there are three squares meeting at each corner of a cube. So the more you know about polyhedra, the more modular origami shapes you can make.
A 3D polyhedron is a shape made up of polygons for sides, where a polygon is a shape made up of line segments connected in a row, such as a triangle or a square.
The Platonic Solids are five convex polyhedra that have been known since the time of Plato, the cube, the tetrahedron, the octahedron, the dodecahedron and the icosahedron, pictured on p iv. Each of these polyhedra has all of its faces the same regular polygon which means also that all of its edges are the same length. It can be shown that these are the only five geometric shapes with these properties. In addition, their vertices all lie on a sphere.
In Platos times the Platonic solids were equated with the following elements: tetrahedron-fire; cube-earth; octahedron-air; icosahedron-water and dodecahedron-universe. In the 1600s, Johannes Kepler used them as a basis for his system of astronomy. During the Renaissance artists used them as the subject of their art to better understand perspective. Starting in the 1800s polyhedra were used as models for crystal structures. Haeckel in the 1800s drew pictures of radiolaria which have icosahedral shape. In the 20th century virus coats were found to be icosahedral, fullerenes are molecules based on other polyhedral shapes, scientists used nanotechnology to build molecules of polyhedral shapes. Many 20th century artists and sculptors incorporated polyhedra into their work.
- Cromwell, Peter; Polyhedra; Cambridge University Press, 1997
- Fuse; Unit Polyhedron Origami, Japan Publications, 2006
- Fuse; Unit Origami, Japan Publications, 1990
- Gurkewitz and Arnstein, 3D Geometric Origami: Modular Polyhedra; DoverPublications, 1996
- Gurkewitz and Arnstein, Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, Dover Publications, 2003
- Kawamura; Polyhedron Origami for Beginners, Japan Publications, 2002
- Mitchell; Mathematical Origami; Tarquin Publications, 1997
- Montroll; Constellation of Origami Polyhedra; Dover Publications, 2004
- Montroll; A Plethora of Polyhedra in Origami; Dover Publications, 2002
- Mukerji; Marvelous Modular Origami; AKPeters, 2007
- Simon, Arnstein and Gurkewitz; Modular Origami Polyhedra; Dover Publications, 1999
- Wenninger, Magnus; Polyhedron Models; Cambridge University Press, 1970
| Krystyna Burczyk | www1.zetosa.com.pl/burczyk/origami/galery1-en.htm |
| George Hart | www.georgehart.com/ |
| Tom Hull | www.merrimack.edu/~thull/ |
| David Mitchell | www.origamiheaven.com |
| Jeannine Mosely | world.std.com/~j9/sponge/ |
| Meenakshi Mukerji | home.comcast.net/~meenaks/origami |
| Mette Pederson | mette.pederson.com/ |
| David Petty | members.aol.com/ukpetd/ |
| James Plank | www.cs.utk.edu/~plank/plank/origami/origami.html |
| Francis Ow | web.singnet.com.sg/~owrigami/ |
| Eric Weisstein | mathworld.wolfram.com/origami.html |
| Magnus Wenninger | employees.csbsju.edu/mwenninger/ |
| Joseph Wu | www.origami.as/home.html |
| British Origami Society | www.britishorigami.info |
| Origami-USA | www.origami-usa.org/ |
| - - - - - - - - - - - | Valley crease, points down |
 | Mountain crease, points up |
 | Fold a valley crease |
 | Unfold |
 | Fold a valley crease and unfold |
 | Fold away from you, making a mountain crease |
 | Unfold a mountain crease |
 | Repeat once |
 | Repeat on the back |
 | Repeat three times |
 | Turn over |
 | Apply pressure here |
 | The next figure shows what this eye sees |
 | Inside reverse sink here, or just push in |
| ............... | Hidden line |
 |
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