A small rhombicosidodecahedron is a shape with 62 faces, 120 edges, and 60 vertices. It's a cantellation of an icosahedron or dodecahedron. This shape is usually just called a rhombicosidodecahedron. A great rhombicosidodecahedron is a shape with 62 faces, 180 edges, and 120 vertices. It is a truncated icosidodecahedron, and is usually called a truncated icosidodecahedron.

A snub icosidodecahedron, also known as a "snub dodecahedron" or a "snub icosahedron", has 92 faces.

it has 30 vertices

It has 60 edges.