Dodecahedron and icosahedron
Dodecahedron and icosahedron are dual polyhedra: the centres of the faces of a icosahedron are the vertices of a dodecahedron.
The vice versa; is also true; otherwise, we can dispose the two polyhedra so that there is a sphere tangent to all their edges.
The image has been used in the exhibition Simmetria, giochi di specchi - Symmetry, playing with mirrors.
The image belongs to the sections...:
Duality (3D geometry)
The symmetry group of the dodecahedron (*532) (Symmetry)