Here is a nested series of seven spheres which can rotate freely, independently of each other. This construction is an homage to the long tradition of turning concentric ivory spheres on a lathe. As outlined on this page, this artistic tradition started in Nuremburg in the seventeenth century and is still carried out in parts of Asia.

Each sphere is based on the edges of a different Goldberg polyhedron. From inside to inside, they are: 
2, 0 (42 faces); 
2, 1 (72 faces); 
3, 0 (92 faces); 
2, 2 (122 faces); 
3, 1 (132 faces); 
4, 0 (162 faces); 
3, 2 (192 faces); 

When built, the twelve pentagons are aligned in all the spheres, so you can look right through them in to the center and out the other side. After randomizing the orientations, it is something of a puzzle to restore this property.