In geometry, how many different types of platonic solids are there?

Platonic solids are three-dimensional geometric shapes whose faces are all identical. There are only 5 Platonic solids, which are tetrahedrons, hexahedrons, octahedrons, dodecahedrons and icosahedrons. A dice, for example, must be a platonic solid, so that when it lands, only one numbered side faces upwards.

The Greek philosopher Plato wrote about the shapes in his work 'Timaeus' (c.360 BC). He associated four of the shapes with each of the classical elements. A tetrahedron, which has 4 triangular sides and looks like a pyramid is associated with fire. Earth is a hexahedron, also known as a cube. The right-sided octahedron represents air, and water is an icosahedron, a 20-sided shape. The fifth shape, the 12-sided dodecahedron, is associated with the cosmos and may resemble the shape of the universe.

Theaetetus, a contemporary of Plato, also wrote about the shapes and was the first to determine there could only ever be five. Despite his involvement, the shapes are named only after Plato. Theaetetus gave a mathematical description of all five shapes rather than associate them with the elements.