Johannes Kepler thought he had hit upon a secret of the
universe, a demonstration of the guiding hand of God (and
geometry) in the structure of the heavens. In his _Mysterium
Cosmographicum_ (see http://en.wikipedia.com/wiki/Johannes_Keple
r#Mysterium_Cosmographicum), he showed how the (circular) orbits
of the planets could be shown to correspond to the five Platonic
regular solids, nested inside and outside the spheres containing
the orbits. It's an elegant theory, consonant with the idea of
perfection in the heavens, and even explains why there were only
six planets (because there are only five convex regular solids).
Of course, for all its beauty and elegance, the theory is
*wrong*, and indeed there is no relationship between the
Platonic solids and the orbits of the planets, and the planets
don't even move in circles, and there are more than six of them.
Still, here is a model of Kepler's original idea, rendered in
thin wires. The spheres of the planets' orbits are suggested by
half-spheres of eight spokes