Rhombicosidodecahedron-c. Vertices 60.

All segments
[size=85][url=http://dmccooey.com/polyhedra/Rhombicosidodecahedron.html]Rhombicosidodecahedron[/url] [br]Vertices: 60 (60[4])[br]Faces: 62 (20 equilateral triangles + 30 squares + 12 regular pentagons)[br]Edges: 120[/size]

Information: Rhombicosidodecahedron-c. Vertices 60.