Platonic solids and Euler's formula

There are exactly five regular polyhedra, the Platonic solids. A line of reasoning about the angles around a vertex explains why there are only five, while Euler’s formula $V-S+F=2$ links the vertices, edges and faces of every convex polyhedron. It closes with an example on the cube, with the main diagonal and the hexagonal cross-section.

• The five Platonic solids
• Euler’s formula
• The cube - diagonal and hexagonal cross-section