English | October 26, 2014 | ISBN: 150308485X | 80 Pages | EPUB | 1.16 MB

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 areThe history of the discovery of Platonic solidsThe common features of all Platonic solidsThe geometrical details of each Platonic solidExamples of where each type of Platonicsolid occurs in natureHow we know there are only five types of Platonic solid (geometric proof)A topological proof that there are only five types of Platonic solidWhat are dual polyhedronsWhat is the dual polyhedron for each of the Platonic solidsThe relationships between each Platonic solid and its dual polyhedronHow to calculate angles in Platonic solids using trigonometric formulaeThe relationship between spheres and Platonic solidsHow to calculate the surface area of a Platonic solidHow 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.

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