There are 5. They are the tetrahedron (4 triangular faces), the cube (6 square faces), the octahedron (8 triangular faces), the dodecahedron (12 pentagonal faces), and the icosahedron (20 triangular faces).
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There are different numbers on the different platonic solids.
Because 6 platonic solids would be too many, and 4 wouldn't be enough
The book called Platonic Solids: The experience
We don't know for certain who discovered the platonic solids first. However, Pythagoras is credited by some sources as discovering the platonic solids first. Other sources credit Theaetetus as being the first to describe all five platonic solids and proving that these are the *only* platonic solids.
The Platonic solids were name after the Greek philosopher Plato, who theorized that the classical elements were constructed from the regular solids.