How did Johannes Kepler use the five regular polyhedrons in his early model of the solar system?

In his 1596 work Mysterium Cosmographicum ("Cosmographic Mystery"), Johannes Kepler utilized the five Platonic solids—the tetrahedron, cube, octahedron, dodecahedron, and icosahedron—to explain the structure of the solar system.123

Kepler sought to understand why there were exactly six known planets. He proposed that these five regular polyhedra served as geometric spacers between the concentric spheres of the planetary orbits. By nesting these solids within one another, he believed he had uncovered the divine "cosmic architecture" of the heavens.13

While this early model was intended to define the arrangement of the universe, Kepler’s subsequent efforts to reconcile his theory with the precise observational data of Tycho Brahe ultimately led him away from this rigid geometric framework. His rigorous analysis of these observations forced him to abandon circular orbits in favor of his laws of planetary motion, which established that planets move in ellipses.13