Platonic Solids · 3D
Tetrahedron
{3,3} · Fire
Four triangles: the simplest possible solid, and the most stable frame in nature. Plato gave it to fire, for its sharp points.
- Vertices
- 4
- Edges
- 6
- Faces
- 4
- Dihedral
- 70.53°
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
- It is its own dual: swap faces and vertices and you get another tetrahedron.
- Two interlocked tetrahedra make the star tetrahedron (Merkaba).
- Seen straight down one corner, its shadow is a triangle with a “Y” inside.
- Methane (CH₄) and diamond bonds point to the corners of a tetrahedron.
History and meaning
In the Timaeus (about 360 BCE) Plato assigned the five regular solids to the elements. The tetrahedron is fire: the lightest, sharpest, most mobile.
Across the dimensions
- Cell of 5-CellAdd a fifth point in the fourth direction, joined to all four: the 5-cell, with this tetrahedron as one of its five cells.
- Dual Itself: it is self-dual.
Learn it step by step
- Journey FlatlandStep 3: A square in a tetrahedron
