Amazing Math: Introduction to Platonic Solids

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.