The Platonic solids have fascinated the intellectually curious (and those with little else to do) for several thousand years. Leonardo returned to them time and again and they seem to have served as a useful tool for stimulating his thought processes.

For anyone who wasn’t quite paying attention at school on the day the Platonic solids were discussed, we’ll recap.

A Platonic solid is a three dimensional object formed entirely from regular polygons, such as triangles, squares or pentagons. Since ancient times, ie when Plato was about, there have only ever been five, and even back then top mathematician Euclid was able to prove that there can never be any more than five. (Anyone who really wants to know why this is the case should find a good library on a wet afternoon and look up Book XIII of Euclid’s Elements.)

Plato believed that four of these solids represented the atomic structure of the classical elements (fire, earth, air and water). Although he was mistaken, some of them are, in fact, the same shape as certain crystals. Sodium chloride (table salt) has crystals which are cube shaped, calcium fluoride crystals come in the form of octahedra while pyrite crystals grow into dodecahedra.