The Platonic Solids Book

This manual features 17 easy-to-master projects involving the Platonic solids: the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Includes detailed diagrams and photos of all the completed models.

This book contains a meticulous geometric investigation of the five Platonic Solids and five other important polyhedra, as well as reference charts for each solid. (Mathematics)

In this introduction to the techniques of bookbinding, Franz Zeier guides readers step-by-step through projects for making a variety of boxes, portfolios, book covers, photograph albums, mats, and sewn and adhesive

This book is a guide to the 5 Platonic solids (regular tetrahedron, cube, regular octahedron, regular dodecahedron, and regular icosahedron). These solids are important in mathematics, in nature, and are the only 5 convex regular polyhedra that exist. Topics covered include: What the Platonic solids are The history of the discovery of Platonic solids The common features of all Platonic solids The geometrical details of each Platonic solid Examples of where each type of Platonic solid occurs in nature How we know there are only five types of Platonic solid (geometric proof) A topological proof that there are only five types of Platonic solid What are dual polyhedrons What is the dual polyhedron for each of the Platonic solids The relationships between each Platonic solid and its dual polyhedron How to calculate angles in Platonic solids using trigonometric formulae The relationship between spheres and Platonic solids How to calculate the surface area of a Platonic solid How to calculate the volume of a Platonic solid Also included is a brief introduction to some other interesting types of polyhedra - prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra. Some familiarity with basic trigonometry and very basic algebra (high school level) will allow you to get the most out of this book - but in order to make this book accessible to as many people as possible, it does include a brief recap on some necessary basic concepts from trigonometry.

Adapted from his computer-animated video, Platonic Solid Rock, Dan Radin's The Platonic Solids Book combines beautiful 3-D computer graphics with an insightful and entertaining journey through the mathematics and recreations of polyhedra. Paper templates and detailed instructions guide the reader through the construction of the Platonic solids, the compounds of the Platonic solids, and an origami star polyhedron. The reader is led through an exploration of the philosophical nature of mathematics in the contexts of polyhedra. Chapters end with guiding questions for the reader to ponder. Finally, an appendix contains six lesson plans that can be adapted to teach students from elementary school through college. The Platonic Solids Book is an excellent textbook, reference book, teacher's resource, and recreational reading for the amateur or seasoned geometer.

Polyhedra are incredibly beautiful shapes. Illustrated step-by-step diagrams show how to fold a collection of around 30 models including the five Platonic Solids, sunken versions of each, models with color patterns, variations on Archimedean Solids, and more. Each model is folded from a single uncut square. They range from simple to complex.

How can you build sturdy Platonic solids that will hold together through to the last gluing? The templates in this book were designed to answer that question. You can build the solids directly from the templates, or use them as a model to create the solids out of colored paper, cardboard, or paper you have colored or painted yourself. The completed solids made from the templates are about 1.6inches (4cm) high, and you can also follow the instructions to build larger solids. Each template is included in the book three times, allowing you to practice or build them along with your friends. Includes 3x5 black-and-white templates for building Platonic solids and instructions, and clear step-by-step images for ruler and compass constructions on how to draw the templates. * New in the second edition: * Some of the template images were moved to the same pages for easier copying for teachers. * Detailed drawing instructions for ruler and compass constructions.