What are the three types of polygons that can be the faces of a Platonic solid?

The polygons are the equilateral triangle, the square, and the regular pentagon.

The faces of these platonic solids are made from the following polygons:

tetrahedron - 4 triangles

cube - 6 squares

octahedron - 8 triangles

dodecahedron - 12 pentagons

icosahedron - 20 triangles