27. The idea of a middle point is applicable to each world severally, not to the confederation of worlds. 28. The case of the ‘stone outside the world’ (the moon?), which some regard as no part of our earth, and therefore not bound to move towards it. The paradoxical views of Chrysippus. 29. The Stoic difficulty as to Zeus or Providence in the plural met. Why not a choir of such powers, free to range from part to part of the universe? 30. Such a view of deities sociable and free to communicate with each other is the grander one. 31. (PHILIPPUS asks to have the bearing of the number five and the five solid figures on Plato’s scheme explained.) 32. LAMPRIAS: The matter is thus explained by Theodorus of Soli:[128] There are five and no more solid figures having all the faces and all the solid angles in each equal. These are— (_a_) The Pyramid (Tetrahedron) with four faces, each an equilateral triangle, and four solid angles, (_b_) The Cube, six faces, each a square, and eight solid angles, (_c_) The Octahedron, eight faces, each an equilateral triangle, and six solid angles, (_d_) The Dodecahedron, twelve faces, each a regular pentagon, and twenty solid angles, (_e_) The Eicosahedron, twenty faces, each an equilateral triangle, and twelve solid angles. [It follows that (_d_) having more, and blunter, solid angles than any, most nearly approximates to the Sphere. (And, in fact, if the content of the Sphere be 100, that of (_d_) is 66·5, that of (_e_) only 60·5, that of (_c_) 36·75, and so on). Plato (_Timaeus_, pp. 53-5, where see Archer-Hind) shows that each equilateral triangle may easily be broken into six ‘primary scalenes’, i. e. triangles with angles 90°, 60°, 30°, which again will reproduce themselves _ad infinitum_ (Euclid, 6, 8). Hence, if a universe be constructed out of (_a_) or (_c_) or (_e_) or their plane faces, or of all of these, it can, in case of dissolution, be reconstructed. This does not apply to the Cube, the faces of which, however, yield isosceles right-angled triangles, also available as ‘constituents’ in infinite number, nor yet to (_d_) which is therefore reserved for another purpose, as to which see Burnet (_Early Greek Philosophers_, c. 7, sect. 148).] The solid figures may be used to construct five different worlds, or omitting (_d_) for the four ‘elements’ (fire, &c.). 33. AMMONIUS criticizes; he points out that the difficulty about the figure (_d_) has been ignored. 34. LAMPRIAS drops the subject for the present, and turns to the five categories of being in the _Sophistes_ and _Philebus_. It is reasonable to assume that the physical universe may correspond. 35. Consider the Pythagorean first principles of number and the origin of the number five out of the first odd and the first even. 36. Five senses, five fingers, five planets (the sun with the two inner planets taken as one).