Whether the geometric cosmos made up of mandalas, spheres, squares and other colors and shapes is how planets & stars appear with a higher vision or they are just psychological keys to those realms or something else, I know not. The fact that such a similar use of geometric shapes was shared by Buddhism & Platonism, for example, suggests that neither a mere lack of telescopes nor fantastic imaginations were the causes.
From a sketch about Plato's cosmology in his Timaeus:
In accordance with the requirements for the construction of the body of the universe previously set out at 31b4–32c4, the Craftsman begins by fashioning each of the four kinds “to be as perfect and excellent as possible…” (53b5–6). He selects as the basic corpuscles (sômata, “bodies”) four of the five regular solids: the tetrahedron for fire, the octahedron for air, the icosahedron for water, and the cube for earth. (The remaining regular solid, the dodecahedron, is “used for the universe as a whole,” [55c4–6], since it approaches most nearly the shape of a sphere.) The faces of the first three of these are composed of equilateral triangles, and each face is itself composed of six elemental (scalene) half equilateral right-angled triangles, whose sides are in a proportion of 1:√3:2. Timaeus does not say why each face is composed of six such triangles, when in fact two, joined at the longer of the two sides that contain the right angle, will more simply constitute an equilateral triangle. The faces of the cube are squares composed of four elemental isosceles right-angled triangles and again, it is not clear why four should be preferred to two. Given that every right-angled triangle is infinitely divisible into two triangles of it own type (by dropping a perpendicular from the right-angle vertex to the hypotenuse, the resulting two smaller right triangles are both similar to the original triangle) the equilateral or square faces of the solids and thus the stereometric solids themselves have no minimal size. Possibly, then, the choice of six component triangles for the equilateral and four for the square is intended to prevent the solid particles from becoming vanishingly small. Since each of the first three of the regular solids has equilateral faces, it is possible for any fire, air or water corpuscles to come apart in their interactions—they cut or crush each other—and their faces be reconstituted into corpuscles of one of the two other sorts, depending on the numbers of faces of the basic corpuscles involved. For example, two fire corpuscles could be transformed into a single air corpuscle, or one air corpuscle into two fire corpuscles, given that the tetrahedron has four faces and the octahedron eight (other examples are given at 56d6–e7). In this way Timaeus explains the intertransformation that can occur among fire, air and water. On the other hand, while the faces of the cube particles may also come apart, they can only be reconstituted as cubes, and so earth undergoes no intertransformation with the other three. Having established the construction and interactive behavior of the basic particles, Timaeus continues the physical account of the discourse with a series of applications: differences among varieties of each of the primary bodies are explained by differences in the sizes of the constituent particles (some varieties consisting of particles of different sizes), and compounds are distinguished by their combinations of both different sorts and different sizes of particles. These various arrangements explain the perceptible properties the varieties of primary bodies and their compounds possess. An object's particular arrangement of triangles produces a particular kind of “disturbance” or “experience” (pathos) in the perceiving subject, so that the object is perceived as having this or that perceptible property.