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The Platonic Solids

What are they?

The five Platonic Solids have been known to us for thousands of years. These five special polyhedra are the tetrahedron, the cube, the octahedron, the icosahedron, and the dodecahedron. You might be surprised to find out that they are the only convex, regular polyhedra (if you want to read the definitions of those words, see the vocabulary page).

What do they look like?

You can see pictures of all five Platonic solids.

Why are they called that?

The Greek philosopher Plato, who was born around 430 B.C., wrote about these five solids in a work called Timaeus. Historical accounts vary a little, but it is usually agreed that the solids themselves were discovered by the early Pythagoreans, perhaps by 450 B.C. There is evidence that the Egyptians knew about at least three of the solids; their work influenced the Pythagoreans.

In any case, Plato mentioned these solids in writing, and it was he who identified the solids with the elements commonly believed to make up all matter in the universe. In Plato's times, people believed that all things were made up of five different atoms. They were fire, air, water, earth, with the fifth being the cosmos (the universe itself)

Plato identified fire atoms with the tetrahedron, earth atoms with the cube, air atoms with the octahedron, water atoms with the icosahedron, and the cosmos atoms with the dodecahedron.

Find out how the Platonic Solids are made.
What is the Euler Number of a polyhedron? You will find that the Archimedean Solids are related to the Platonic solids in interesting ways.