Polygons and PolyhedraPlatonic

At the beginning of this course we defined regular polygons as particularly “symmetric” polygons, where all sides and angles are the same. We can do something similar for polyhedra.

In a regular polyhedron all faces are all the same kind of regular polygon, and the same number of faces meet at every vertex. Polyhedra with these two properties are called Platonic solids, named after the Greek philosopher Plato.

So what do the Platonic solids look like – and how many of them are there? To make a three-dimensional shape, we need at least faces to meet at every vertex. Let’s start systematically with the smallest regular polygon: equilateral triangles: