1st Edition

Origami Polyhedra Design

By John Montroll Copyright 2011
    302 Pages
    by A K Peters/CRC Press

    302 Pages
    by A K Peters/CRC Press

    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.

    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


    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