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

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.