Publisher's Synopsis
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