Symmetry and Beauty in Plato

Plato writes about Beauty in many of his dialogues, particularly in the Symposium, but he has no word equivalent to our "Symmetry", and this concept was not then formalised. Nevertheless, there are indications that some aspects of the concept were understood, if only intuitively. Plato has a very abstract concept of beauty, and when he uses "beauty" to characterise the so-called "Platonic Solids" in the Timaeus, he seems to be emphasising at least their regularity. It can be argued that the way in which he specifies the detailed construction of the solids is remarkably close to a modern description in terms of (point) symmetry. For Plato, something of our symmetry is included in what he means by beauty, and the long mathematical approach to symmetry starts with the Timaeus.