Origami Polyhedra Design

Part I: Designing Origami Polyhedra Polyhedra Overview Design Factors and Techniques Math and Design Design Method Examples Polygons Equilateral Triangle Pentagon Hexagon Heptagon Octagon Silver Rectangle Bronze Rectangle Golden Rectangle Part II: Platonic and Related Polyhedra Tetrahedron Design Tetrahedron Duo-Colored Tetrahedron Striped Tetrahedron Tetrahedron of Triangles Stellated Tetrahedron Dimpled Truncated Tetrahedron Cube Design Cube Striped Cube Triangles on Cube Cube with Squares Stellated Octahedron Cubehemioctahedron Dimpled Rhombicuboctahedron Stacked Cubes Octahedron Design Octahedron Striped Octahedron Duo-Colored Octahedron Stellated Cube Octahemioctahedron Dimpled Truncated Octahedron More Platonic Solids Design Icosahedron Dodecahedron 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 Heptahedron 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 is respected for his work in Origami throughout the world. His published work has significantly increased the global repertoire of original designs in Origami. John is also acknowledged for techniques such as the double-rabbit ear fold and for ground-breaking bases like the Dog Base and the Insect Base. The American Origami master is known for being the inspiration behind the single-square, no cuts, no glue approach in Origami. John started folding in elementary school. He quickly progressed from folding models from books to creating his own designs. Since his first published book, Origami for the Enthusiast, John has written many more books. Each model that John designs has a meticulously developed folding sequence. John's long-standing experience allows him to accomplish a model in lesser number of steps rather than plenty. It is his constant endeavor to give the reader a pleasing folding experience.

! 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