Renowned German mathematician, astronomer and astrologer Johannes Kepler (1571-1630) believed that the relationships between the 5 platonic solids governed the order of the universe. This is an interactive 3D view illustrating Kepler’s ideas.
Kepler believed in a geometrical basis for the universe and thought the planets were arranged in their orbits through the relationships between the five “perfect” three-dimensional forms. He turned out to be wrong, but in the process of trying to prove his theory he laid down the foundation for modern astronomy.
This particular model of the nested Platonic solids was proposed by renowned mathematician John H. Conway.
Zometool offers a kit for constructing this model. (Most of the content on this page is excerpted from that page.) You might also enjoy the instructions, which pack in a ton of information.