Amazing Math: Introduction to Platonic Solids

This book is a guide to the 5 Platonic solids (regular tetrahedron, regular 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.

• 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
  
• An introduction to some other interesting types of polyhedra – prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra.
  

Note: 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, I have included a brief recap on some necessary basic concepts from trigonometry (such as sine, cosine, radians, etc.).