Here the Tetrahedron (purple), Octahedron (green), Dodecahedron (blue) and the Icasohedron (yellow) are all inscribed within a Cube (orange).

Each inscribed figure has some element that lies on the cubes face: i.e. all the Tetrahedron's edges, all the Octahedrons vertices, 6 of the Dodecahedron's edges, and 6 of the Icocahedrons edges. The Tetrahedron also shares all its vertices with the Cube.

The Dodecahedron and Icosahedron are shown in their dual relationship.