There are just five platonic solids.

From equilateral triangles you can make:
with 3 faces at each vertex, a tetrahedron;
with 4 faces at each vertex, an octahedron;
with 5 faces at each vertex, an icosahedron.

From squares you can make:
with 3 faces at each vertex, a cube.

From pentagons you can make:
with 3 faces at each vertex, a dodecahedron.