Cube and octahedron

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Cubes and octahedra are dual polyhedra. The centres of the faces of a cube are vertices of an octahedron and vice versa. You can also construct the two polyhedra so that they have the tangent sphere in common with all their edges.
This picture has been used at the exhibition Simmetria, giochi di specchi - Symmetry, playing with mirrors.

© matematita

The image belongs to the sections...:
From "towards the 4th dimension" (From "XlaTangente")
Duality (3D geometry)
The symmetry group of the cube (*432) (Symmetry)