First of all, what is a Platonic solid? Platonic solids are regular polyhedral in Euclidean Geometry which their faces are regular polygons of the same number of sides and same size. Among the countless shapes, there are only 5 polyhedral shapes that meet these demands: The Tetrahedron, the Hexahedron (AKA cube), the Octahedron, the Dodecahedron and the Icosahedron. The names comes from the Greek numbers 4 (Tetra-), 6 (Hexa-), 8 (Octa-), 12 (Dodeca-) and 20 (Icosa-) to represent the number of faces.
And you may now wonder, how did Plato knew that there is not some sort of Triakosahiliahedro (300.000 faces) that meets these demands? Its the magic of Geometry, and of course the magic of logic thought. Watch the video...