 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.[29]