Design Nomenclature / Form & Geometry
Platonic solid
Also called regular polyhedron, regular solid, tetrahedron, icosahedron
This entry has not been translated yet and is shown in English.
One of exactly five convex polyhedra whose faces are congruent regular polygons meeting identically at every vertex: tetrahedron, cube, octahedron, dodecahedron, icosahedron. Five is a proof, not a survey — the face angles at a vertex must sum below 360°, which admits no sixth. Duality pairs them: cube with octahedron, dodecahedron with icosahedron, tetrahedron with itself.
Origin
Named for Plato, who in the Timaeus assigned four of them to the classical elements and the dodecahedron to the cosmos. Euclid's Elements ends with the construction of all five and the proof that there are no more.