Platonic Solids

name

cube

dodecahedron

icosahedron

octahedron

tetrahedron

transparency

color

There are only five convex polyhedra with identical regular convex faces, as proved in Euclid's Elements. All their vertices lie on a sphere, all their faces are tangent to another sphere, all their edges are tangent to a third sphere, all their dihedral and solid angles are equal, and all their vertices are surrounded by the same number of faces.