## Rabbit holes

Da Vinci

Divine proportion

Dodecahedron

Dymaxion

Euclid

Golden mean

Hexagon

Icosahedron

Icosidodecahedron

Making a lamp

Motivation

Octagon

Pentagon

Pacioli

Paper

Plato

Rhombicosido-

decahedron

Rhombicub-

octahedron

Symmetry

Truncation

Wood

Zometool

# The dodecahedron – 6

## Plato and the dodecahedron

As the ancient Greek mathematicians began to explore three-dimensional space, they discovered that there are five regular solids (or polyhedrons) that can be formed from regular polygons, for example, the cube is formed from squares. Of these five, three are based on equilateral triangles, one on squares, and one on pentagons.

Plato attributed philosophical significance to these five solids, and they came to be known as the Platonic solids. He associated the four elements—air, earth, water, and fire—with the four solids made from triangles and squares.

The pentagon-based dodecahedron symbolized the heavens to Plato: "There still remained a fifth construction, which the gods used for embroidering the constellations on the whole heaven."