It has 122 faces: 20 triangles, 60 squares, 12 pentagons, and 30 rhombs.
The 120 vertices exist at two sets of 60, with a slightly different distance from its center.
It can also be constructed as a rectified rhombicosidodecahedron.
The expansion operation from the rhombic triacontahedron can be seen in this animation: This polyhedron can be dissected into a central rhombic triacontahedron surrounded by: 30 rhombic prisms, 20 tetrahedra, 12 pentagonal pyramids, 60 triangular prisms.
If the central rhombic triacontahedron and the 30 rhombic prisms are removed, you can create a toroidal polyhedron with all regular polygon faces.