Platonic Solids — What is a Platonic Solid?

A Platonic Solid is a regular, convex polyhedron in a three-dimensional space with equivalent faces composed of congruent convex regular polygonal faces. Some sets in geometry are infinite, like the set of all points in a line. Platonic solids, however, are a finite set of only five, three-dimensional shapes. The five solids that meet this criterion are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

Here are the five Platonic Solids:

1. Tetrahedron has 4 triangular faces
2. Cube has 6 square faces
3. Octahedron has 8 triangular faces
4. Dodecahedron has 12 pentagonal faces
5. Icosahedron has 20 triangular faces.

The 5 Platonic Solids

The Platonic solids are prominent in the philosophy of Plato, their namesake. Plato wrote about them in the dialogue Timaeus c. 360 B.C. in which he associated each of the four classical elements (earth, air, water, and fire) with a regular solid. Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron.

Of the fifth Platonic solid, the dodecahedron, Plato obscurely remarked, “…the god used [it] for arranging the constellations on the whole heaven”.