XXXII. ‘Yes,’ said I, ‘yet Theodorus of Soli seems to treat the argument very fairly, in expounding the Mathematics of Plato. This is his method: the Pyramid, the Octahedron, the Eicosahedron and the Dodecahedron, the solid figures which Plato ranks first, are all beautiful because of the symmetry and equality of their formulae; nothing better than these or equal to them has been left over for Nature to compose [Sidenote: B] or to frame. They have not, however, all been constructed on a single plan, nor have all a similar origin. The Pyramid is the finest and smallest, the largest and the one of most parts is the Dodecahedron; of the remaining two the Eicosahedron is more than double the Octahedron in number of triangles.[171] It follows that it is impossible for all to take their origin at once from one and the same matter. For those which are fine and small, and more simple in their structures, must be the first to obey him who stirs and fashions the mass; they must sooner cohere and be completed than those whose parts are abundant, and the figures complex, and their construction more laborious, [Sidenote: C] as the Dodecahedron. It follows that the Pyramid is the only primal body, and that none of the others is so; they are left behind by Nature in the becoming. For this strange result there is, however, a remedy, the division and distribution of matter into five worlds. Here the Pyramid (for it first formed substance), there the Octahedron, in a third world the Eicosahedron. But from the figure which first took substance in each the rest will take their origin, all change arising by concretion or dissolution of parts, as Plato himself shows.[172] He goes thoroughly into nearly all the cases, but for us a brief survey will suffice. Since air is formed when fire is extinguished, and when rarefied [Sidenote: D] again yields fire out of itself, we must observe what happens to the seeds of either element, and the changes. The seeds of fire[173] are the Pyramid with its twenty-four primary triangles; the seeds of air are the Octahedron with its forty-eight. Therefore one element of air is formed by the commixture and coherence of two of fire; and one of air is exchanged into two of [Sidenote: E] fire, or by close pressure into itself passes away into the form of water. Thus, universally, that which is first formed readily allows the others to come into being by transmutation. It is not the case that one is first; different elements in different structures give the initial and prerogative movement into being, yet the common name is kept throughout.’