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_Kepler#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, and the solids are rendered in wireframe nesting within them. Because of the thickness of the wires, the solids and the spheres overlap a little—a feature which, I hope, keeps the model together. There are also some support wires, two running across the top of the spheres and one down through their pole.
An initial print has proved... not as bad as might be. The thin "wires" of WSF material are somewhat too flexible for the project, but only on the outermost shapes (the outermost sphere and especially the cube). The inner ones, even the tetrahedron, are fairly sturdy and rigid enough. I've thickened the wires of the cube and also added an "X" of supporting struts on each face of the cube and attached them to the next smaller sphere, and a "Y" of them on each face of the tetrahedron for good measure. I also put two more rings on the outermost sphere for more stability and added a base so that it has something to stand on. Might still be a little wobbly, but everything added makes it more expensive, so I'm hoping to do more with less. Have not yet printed the new version.