Platonic Polyhedra

The formal study of polyhedra can be said to begin with Pythagoras and his followers in the 6th century BCE. Theaetetus (417–369 BCE) then provided the first rigorous mathematical description of all five and mathematically proved that only five regular convex polyhedra can possibly exist in three-dimensional space.

U01 Tetrahedron
01 - Tetrahedron
V: 4  |  E: 6  |  F: 4
Vertex Config: 3 · 3 · 3
Bowers: tet  |  TOCID: T
Wythoff: 3 | 2 3
Kaleido: K06  |  Wenninger: 1
U05 Octahedron
05 - Octahedron
V: 6  |  E: 12  |  F: 8
Vertex Config: 3 · 3 · 3 · 3
Bowers: oct  |  TOCID: O
Wythoff: 4 | 2 3
Kaleido: K10  |  Wenninger: 2
U06 Cube
06 - Cube
V: 8  |  E: 12  |  F: 6
Vertex Config: 4 · 4 · 4
Bowers: cube  |  TOCID: C
Wythoff: 3 | 2 4
Kaleido: K11  |  Wenninger: 3
U22 Icosahedron
22 - Icosahedron
V: 12  |  E: 30  |  F: 20
Vertex Config: 3 · 3 · 3 · 3 · 3
Bowers: ike  |  TOCID: I
Wythoff: 5 | 2 3
Kaleido: K27  |  Wenninger: 4
U23 Dodecahedron
23 - Dodecahedron
V: 20  |  E: 30  |  F: 12
Vertex Config: 5 · 5 · 5
Bowers: doe  |  TOCID: D
Wythoff: 3 | 2 5
Kaleido: K28  |  Wenninger: 5