"[T]he Pythagorean construction of the elements was... that... in Plato’s Timaeus. ...[T]here is good reason for believing they only knew three of the regular solids, the , the pyramid (), and the . Plato starts from fire and earth, and... the construction οf the elements proceeds... such... that the and the can easily be transformed into pyramids, while the cube and the dodecahedron cannot. ...[I]t follows that, while air and water pass readily into fire, earth cannot... and the dodecaedron is reserved for another purpose... This would... suit the Pythagorean system; for it would leave room for a dualism... outlined in the Second Part of the poem of Parmenides."