Origami Polyhedra Design

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. As Montroll notes in the introduction, over the past two decades there has been much interest, and several books, on modular origami. 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. There are a total of 72 different designs presented at all levels of difficulty (10 simple, 32 intermediate, 22 complex, and 8 very complex designs). Mathematicians will want to start with regular polygons (the heptagon and octagon are simple designs) and then construct the five Platonic solids (the tetrahedron is a simple design, while the dodecahedron is very complex). In addition to the actual designs, at the beginning of the book, Montroll gives an overview of the theory of polyhedra and the mathematics involved in creating a polyhedral design.

The book is well designed and organized and makes you want to start folding polyhedra. The instructions for the individual models are clear and easy to understand (it does take work to master the folding however). If you already have an interest in origami or polyhedra, this book is for you. Students will be especially interested by the ability to build physical three-dimensional mathematical models from a single sheet of paper.

Tom Hagedorn is Associate Professor of Mathematics at The College of New Jersey.