Short answers, pulled from the story.
The Mysterium Cosmographicum is an astronomy book written by Johannes Kepler that proposes a geometric model of the universe using five Platonic solids. Published in late 1596 at Tübingen, it attempts to explain planetary distances through nested polyhedra and spherical orbs.
Johannes Kepler published the first edition of Mysterium Cosmographicum late in 1596 at Tübingen university. He received copies early in 1597 and began distributing them to prominent astronomers and patrons shortly after publication.
The Mysterium Cosmographicum contains six layers corresponding to Mercury, Venus, Earth, Mars, Jupiter, and Saturn. These layers are created by nesting the five Platonic solids within one another to form unique inscribed and circumscribed spherical orbs.
Johannes Kepler believed his work revealed God's geometrical plan because he viewed the universe as an image of the Trinity with theological convictions about physical and spiritual connections. The Sun corresponded to the Father while the stellar sphere represented the Son and intervening space symbolized the Holy Spirit.
Danish astronomer Tycho Brahe found the ideas intriguing yet unverifiable without his own observations which he had been collecting data for thirty years prior. Kepler sought him out beginning in 1600 after being promised access to these records and received only data on Mars during their meeting.