Origami Polyhedra Design  book cover
1st Edition

Origami Polyhedra Design

ISBN 9781568814582
Published October 26, 2009 by A K Peters/CRC Press
302 Pages

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Book Description

This book unravels the mystery of Geometry in Origami with a unique approach: 64 Polyhedra designs, each made from a single square sheet of paper, no cuts, no glue; each polyhedron the largest possible from the starting size of square and each having an ingenious locking mechanism to hold its shape.

The author covers the five Platonic solids (cube, tetrahedron, octahedron, icosahedron and dodecahedron). There are ample variations with different color patterns and sunken sides. Dipyramids and Dimpled Dipyramids, unexplored before this in Origami, are also covered. There are a total of 64 models in the book. All the designs have an interesting look and a pleasing folding sequence and are based on unique mathematical equations.

Table of Contents

Part I: Designing Origami Polyhedra
Polyhedra Overview
Design Factors and Techniques
Math and Design
Design Method Examples
Equilateral Triangle
Silver Rectangle
Bronze Rectangle
Golden Rectangle
Part II: Platonic and Related Polyhedra
Tetrahedron Design
Duo-Colored Tetrahedron
Striped Tetrahedron
Tetrahedron of Triangles
Stellated Tetrahedron
Dimpled Truncated Tetrahedron
Cube Design
Striped Cube
Triangles on Cube
Cube with Squares
Stellated Octahedron
Dimpled Rhombicuboctahedron
Stacked Cubes
Octahedron Design
Striped Octahedron
Duo-Colored Octahedron
Stellated Cube
Dimpled Truncated Octahedron
More Platonic Solids Design
Sunken Platonic Solids Design
Sunken Octahedron
Sunken Tetrahedron
Sunken Cube
Sunken Dodecahedron
Sunken Icosahedron
Part III: Dipyramids and Dimpled Dipyramids
Dipyramid Design
Triangular Dipyramid 90°
Triangular Dipyramid
Triangular Dipyramid in a Sphere
Tall Triangular Dipyramid
Tall Square Dipyramid
Silver Square Dipyramid
Squat Silver Square Diamond
Pentagonal Dipyramid
Pentagonal Dipyramid 45°
Pentagonal Dipyramid in a Sphere
Golden Pentagonal Dipyramid
Squat Golden Pentagonal Dipyramid
Hexagonal Dipyramid
Silver Hexagonal Dipyramid
Hexagonal Dipyramid 36°
Hexagonal Dipyramid in a Sphere
Squat Silver Hexagonal Dipyramid
Heptagonal Dipyramid
Heptagonal Dipyramid 30°
Heptagonal Dipyramid in a Sphere
Octagonal Dipyramid
Octagonal Dipyramid 26°
Octagonal Dipyramid in a Sphere
Nonagonal Dipyramid
Decagonal Dipyramid
Dimpled Dipyramid Design
Tall Dimpled Square Dipyramid
Dimpled Silver Square Dipyramid
Dimpled Squat Square Dipyramid
Tall Dimpled Hexagonal Dipyramid
Dimpled Silver Hexagonal Dipyramid
Dimpled Hexagonal Dypyramid
Dimpled Hexagonal Dipyramid in a Sphere
Octagonal Flying Saucer
Dimpled Octagonal Dipyramid in a Sphere
Dimpled Octagonal Dipyramid
Dimpled Silver Octagonal Dipyramid

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John Montroll, St. Anselm’s Abbey School, Washington, D.C., USA


... a teacher of geometry because it allows students to fold figures ranging from simple two-dimensional polygons to complex three-dimensional figures ... can easily be blended into the regular classroom curriculum ... an excellent resource. I recommend it for geometry teachers as a supplement to their regular curriculum.
—Gary S. Luck, University of Wisconsin-Milwaukee, Milwaukee, USA

… It covers a truly wide range of objects, including the Platonic polyhedra, di-pyramids and some stellated or ‘sunken’ counterparts. The staggering thing is that each and every example is made of one single sheet of paper. It is astonishing what is possible in the realm of origami. The procedures of generating such a model are explained step by step, which enables the reader to follow the recipe. … I sincerely recommend this nice and absorbing book for all afficionados of origami. …
—O. Roschel, International Mathematical News (IMN), December 2010

Origami's recent explosive increase in sophistication owes much to the pioneering ingenuity of noted origami artist Montroll, as documented by his more than two dozen books published since 1980. ... The present volume collects instructions for folding diverse polyhedra, both convex and concave, including many beautiful variations on Platonic solids, more than 70 models in all. ... Notwithstanding the considerable detail the author provides regarding the matematical proportions, miraculously, the folding processes generally involve no explicit numerical measurement. ... Highly recommended.
—D. V. Feldman, CHOICE, August 2010

Origami Polyhedra Design is a breakthrough collection of original designs created by the author to make polyhedral shapes from a single sheet of paper through folding. In modular origami, a polyhedral shape is built by interlocking many identical origami pieces, where each piece is constructed from a separate sheet of paper. In this book, Montroll, an origami master who pioneered the folding of origami animals from a single sheet of paper, presents methods for folding various polyhedra from a single sheet of paper. The book is well designed and organized and makes you want to start folding polyhedra. ... and the instructions for the individual models are clear and easy to understand...
—Thomas Hagedorn, MAA Reviews, April 2010