Rhombicosacron

A rhombicosidodecahedron is a convex Archimedean solid that has 62 faces: 20 regular triangles, 30 squares, and 12 regular pentagons. It has 120 edges and 60 vertices. Each vertex of a rhombicosidodecahedron has one pentagonal face, two triangular faces, and two square faces meeting at that vertex.