Late ancient Platonists discuss two theories in which geometric entities xplain natural phenomena : the regular polyhedra of geometric atomism and the ccentrics and epicycles of astronomy. Simplicius explicitly compares the status of the first to the hypotheses of the astronomers. The point of omparison is the fallibility of both theories, not the reality of the entities postulated. Simplicius has strong realist commitments as far as astronomy is concerned. Syrianus and Proclus, too, do not consider the polyhedra as devoid of (...) physical reality. Proclus rejects epicycles and eccentrics, but accepts the reality of material homocentric spheres, moved by their own souls. The spheres move the astral objects contained in them, which, however, add motions caused by their own souls. The epicyclical and eccentric hypotheses are useful, as they help us to understand the complex motions resulting from the interplay of spherical motions and volitional motions of the planets. Yet astral souls do not think in accordance with human theoretical constructs, but rather grasp the complex patterns of their motions directly. Our understanding of astronomy depends upon our own cognition of intelligible patterns and their mathematical images. (shrink)