Platonic Solids · 3D
Dodecahedron
{5,3} · Aether
Twelve pentagons, woven from the golden ratio. Plato said the god used it “for arranging the constellations on the whole heaven”.
- Vertices
- 20
- Edges
- 30
- Faces
- 12
- Dihedral
- 116.57°
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane or lift it into four dimensions.
Facts
- Every face is a pentagon, so every diagonal is φ × the edge.
- Five cubes fit inside it, sharing its 20 vertices.
- Its dual is the icosahedron.
- Its 4D cousin, the 120-cell, is made of 120 dodecahedra.
History and meaning
Plato gave the dodecahedron to the cosmos itself; later writers called it the quintessence, or aether. Roman bronze dodecahedra of unknown purpose have been found across Europe.
Across the dimensions
- Cell of 120-CellOne hundred and twenty dodecahedra close into a hypersphere: the 120-cell.
- Dual Icosahedron
Learn it step by step
- Journey The Golden ThreadStep 8: The dodecahedron
