Who Is Plato, and Why Do the Platonic Solids Matter?

Plato was an Ancient Greek philosopher, a student of Socrates and teacher of Aristotle, and the reason five perfectly symmetrical shapes carry his name. If you have seen our Plato's Cubes and wondered who is Plato and what he has to do with a set of coloured blocks, this is the answer. He spent his life asking what lies behind the things we take for granted, and the shapes he wrote about are still the most elegant objects in geometry.

• Who is Plato: an Athenian philosopher (about 428 to 348 BC) often called the father of Western philosophy.
• He founded the Academy, one of the first institutions of higher learning in the Western world.
• The five Platonic solids are the only convex shapes whose faces are all identical regular polygons meeting identically at every corner.
• Plato linked them to the classical elements: fire, earth, air, water and the heavens.

Here is who he was and why the shapes matter.

Plato lived in Athens roughly 2,400 years ago and is best known for his dialogues, written conversations that explore justice, knowledge, beauty and the nature of reality. He studied under Socrates, whose ideas survive mainly through Plato's writing, and later taught Aristotle. He founded the Academy, where mathematics and philosophy were taught together, and its influence runs through every university since. Some credit him as the father of Western philosophy, and even his critics have spent two millennia answering him.

Plato's most famous idea is that behind every imperfect thing we see there is a perfect, unchanging Form. Every drawn circle is a little wobbly, but the idea of a circle is exact. Justice, equality and beauty exist in that same way, he argued: real, but grasped by the mind rather than the senses. It is a strange idea and a powerful one, and mathematicians in particular have never quite let go of it.

They are the only five convex shapes in which every face is the same regular polygon and the same number of faces meet at every corner. There cannot be a sixth. That is not a matter of nobody having found one; it is provable, and Euclid closed his Elements with the proof.

• Tetrahedron: 4 triangular faces. The Ignis.
• Cube (hexahedron): 6 square faces. The Original CMY Cube.
• Octahedron: 8 triangular faces. The Aether.
• Dodecahedron: 12 pentagonal faces. The Mundus.
• Icosahedron: 20 triangular faces. The Motus.

Each has its own character. The tetrahedron is its own dual, meaning that if you place a point at the centre of each face and join them you get another tetrahedron. The cube is the only Platonic solid that can fill space with no gaps, which is why bricks are cubes and not dodecahedra. The dodecahedron is the only one with pentagonal faces, and the icosahedron has the most faces and is the closest to a sphere.

Because their symmetry looked to him like the fingerprint of an ordered universe. In his dialogue Timaeus he matched four of the solids to the four classical elements: the sharp tetrahedron to fire, the stable cube to earth, the octahedron to air and the icosahedron to water. The dodecahedron, with its twelve faces, he reserved for the heavens themselves. The chemistry was wrong, but the instinct was not. Two thousand years later Kepler tried to fit the solids to the orbits of the planets, and today the same shapes turn up in the structure of crystals, viruses and carbon molecules.

Because the questions he asked are still the questions. What is knowledge? What makes something beautiful? Is there an order behind appearances? His shapes are a small, perfect example of his larger idea: that behind the messy world there are forms so exact they could not be otherwise. That is why we named a set of cubes after him, and why the whole CMY range is built on his solids. Pick up one of our polyhedra, hold it to the light and watch cyan, magenta and yellow overlap across faces that Plato would have recognised instantly.

Who is Plato: the Athenian philosopher who taught that perfect forms lie behind imperfect things, and whose name is on the only five shapes that are perfectly regular in three dimensions. Tetrahedron, cube, octahedron, dodecahedron, icosahedron. Everything we make is one of them, and each one still does what he admired: it shows you order you can hold.

Explore Plato's Cubes, and see geometry through a different lens.