In theory the number of Cosmi might be infinite, but a shrinking from the vague ‘Infinity’, in later times associated with the Epicureans, led Plato, for instance, to restrict the number to a possible five. That he based this number upon that of the five regular solids may seem fanciful, but the solid angles and forms observed in crystals might reasonably suggest the hypothesis that the ultimate constituents of the crust of the earth would be found in the most perfect solid structures known to theory. In theory there is much that is attractive in these five solids. To one coming fresh from a study of Plane Polygonal Figures, which exist in infinite number, and, when regular, approximate more and more closely to the Plane Circle, it comes as a surprise to find that, in the next higher degree, the number of solid bodies so approximating to the Sphere is five only. Again, it seems almost a paradox that, of these five, the nearest approximation to the Sphere is attained, not by the body with twenty fine faces, but by that which shews only twelve, and those comparatively blunted and unshapely (pentagons). It was perhaps from such considerations that the Dodecahedron was held of special importance by the Pythagoreans. Plato’s study of the several faces of these solids, as available for construction or reconstruction of a world, leaves nothing to be desired, assuming that a solid body can be built out of plane figures, an assumption which appears to belong to the same habit of thought as that which makes the point the square of unity, and the lineal measure corresponding to the number two the first rectangle. As the pentagon defies the analysis available for the equilateral triangle or for the square, the Dodecahedron remains over, a model or pattern of a stitch-work world, as viewed from outside (_Phaedo_ 110 B and _Timaeus_ 55 C; see also Burnet’s _Early Greek Philosophy_, p. 341 foll.). It may not be amiss to be reminded that Kepler, mathematician as well as astronomer, spent many toilsome years in the endeavour to arrange the members of our solar system upon a plan based on the five solids. ‘If Kepler went out “to seek his father’s asses”, he found a kingdom, for it was in the course of these speculations, and through them, that he discovered not only his own “Third Law”, but also the truth, overlooked by Copernicus, that the orbit of each planet lies in a plane which passes through the centre of the sun.’ (Dreyer, _Planetary Systems_, p. 410.)