The Chemistry of Platonic Triangles

Plato's geometrical theory of what we now call chemistry, set out in the Timaeus, uses triangles, his stoicheia, as the fundamental units with which he constructs his four elements. A paper claiming that these triangles can be divided indefinitely is criticized; the claim of an error here in the commentary by F.M. Cornford is unfounded. Plato's constructions of the elements are analyzed using simple point group theory. His procedure generates fully symmetric polyhedra, but Cornford's 'simpler' alternatives generate polyhedra with low symmetries and multiple isomeric forms. However, Cornford's principle of constructing larger triangles by assembling smaller ones is still valid.