In his Mysterium cosmographicum (1596), Kepler wrote, 

“I undertake to prove that God, in creating the universe and regulating the order of the cosmos, had in view the five regular bodies of geometry known since the days of Pythagoras and Plato, and that he has fixed according to those dimensions, the number of heavens, their proportions and the relations of their movements.”  

The spheres position the planets, with the sequence of perfect solids determining their order and distances.

Although persisting with a vision of harmoniously unifying alchemy, geometry, astronomy, and astrology, Kepler's approach shifted after he began to work under  Tycho. They agreed on a physical unity of the cosmos, but experience with  Tycho moved Kepler to build on precise observations (Tycho's, not his own) rather than purely abstract geometical models.  "The fact is that observation of the celestial motions guides astronomers to the formation of hypothesis in the right way, and not the other way around." As the historian John Christianson describes it,  the approach developed by Tycho and taken up by Kepler was to start with precise observations, interpret a physical meaning with principles of natural philosophy, and then apply mathematics to position the astronomical observations in a model. * The result was to develop models that removed many of the techniques of Copernicus, while developing new hypotheses. The ideal mathematics now would have a solidly phyiscal rationale -- as Copernicus had intended but not supplied.

*  Description and Kepler quotation from John Robert Chistianson, Tycho Brahe and the Measure of the Heavens, London: Reaktion Books, 2020.