The rhombicosidodecahedron was discovered by Archimedes.

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.

Rhombicosidodecahedron

A rhombicosidodecahedron has 20 regular trianglular faces, 30 square faces, 12 regular pentagonal faces. Also has 60 verticies and 120 edges.

A Rhombicosidodecahedron. See the related link for more information.