Plato's Theory of Forms and Geometry

Euclid's geometry was not intended as an exercise in pure geometry, as is now usually assumed, but as a theory of the world. In plato's view, the smallest solids are crystal like elementary particles. And in turn, these particles have faces, which are simple shapes. Hence we have atoms made of Platonic solids and platonic solids made of simple shapes. So it seems clear that atomism can incorporate irrational ideas on forms without contradiction. A hole in the theory that plato thought had caused aristotle to realize that he hadn't solved the problem at all.