The exact time and place of Plato's birth are unknown, but it is certain that he belonged to an aristocratic and influential family. Based on ancient sources, most modern scholars believe that he was born in Athens or Aegina between 429 and 423 BC.
Plato's father was Ariston and his mother was Perictione. Besides Plato himself, Ariston and Perictione had three other children; these were two sons, Adeimantus and Glaucon, and a daughter Potone.
Due to a lack of surviving accounts, little is known about Plato's early life and education. The philosopher came from one of the wealthiest and most politically active families in Athens. Ancient sources describe him as a bright though modest boy who excelled in his studies.
His father contributed all which was necessary to give to his son a good education, and, therefore, Plato must have been instructed in grammar, music, gymnastics and philosophy by some of the most distinguished teachers of his era.
Plato may have traveled in Italy, Sicily, Egypt and Cyrene. Said to have returned to Athens at the age of forty, Plato founded one of the earliest known organised schools in Western Civilization on a plot of land in the Grove of Hecademus or Academus.
The Academy operated until it was destroyed by Lucius Cornelius Sulla in 84 BC. Neoplatonists revived the Academy in the early 5th century, and it operated until AD 529, when it was closed by Justinian I of Byzantium, who saw it as a threat to the propagation of Christianity. Many intellectuals were schooled in the Academy, the most prominent one being Aristotle.
Plato gained an appreciation for mathematics after a series of conversations with his friend Archytas in 388 BC. One of the things that most caught Plato's imagination was the existence and uniqueness of what are now called the five Platonic solids.
Plato was mightily impressed by these five definite shapes that constitute the only perfectly symmetrical arrangements of a set of points in space [not lying in one plane], and late in life he expounded a complete 'theory of everything', in the treatise called Timaeus, based explicitly on these five solids. Interestingly, almost 2000 years later, Johannes Kepler was similarly fascinated by these five shapes, and developed his own cosmology from them.
Along with his teacher, Socrates, and his most famous student, Aristotle, Plato laid the very foundations of Western philosophy and science. Plato appears to have been the founder of Western political philosophy, with his Republic, and Laws among other dialogues, providing some of the earliest extant treatments of political questions from a philosophical perspective.
The Stanford Encyclopedia of Philosophy describes Plato as:
"...one of the most dazzling writers in the Western literary tradition and one of the most penetrating, wide-ranging, and influential authors in the history of philosophy".
Plato associated this form with the element of Fire because of the penetrating acuteness of its edges and vertices, and because it is the simplest and most fundamental of the regular solids.
Plato associated this form with the element of Earth due to the stability and orientation of its square bases. Corresponds to the six directions North, South, East, West, zenith and nadir.
Plato considered this form an intermediary between the tetrahedron, [Fire], and the Icosahedron, [Water] and thus ascribed it to the element of Air. [Considered both hot and wet].
Plato associated this form with Water, the densest and least penetrating of the three fluid elements; Fire, Air and Water. This form has the largest dihedral angles of all the Platonic Solids.
Having detailed the other four solids and ascribed them to the elements, Plato's Timaeus says: "There remained a fifth construction used for embroidering the constellations".