Math: Rhombicosidodecahedron

The rhom-bico-sido-deca-hedron, or small rhombicosidodecahedron, is an Archimedean solid (an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices).

It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices and 120 edges. 20{3}+30{4}+12{5} 3=triangle 4=square 5=pentagon

The name (rhomb(ic)osidodeca)hedron refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the rhombic triacontahedron(30 rhombic faces) which is dual to the icosidodecahedron(20 triangles, 12 pentagons).

If you blow up an icosahedron by moving the faces away from the origin the right amount, without changing the orientation or size of the faces, and do the same to its dual dodecahedron, and patch the square holes in the result, you get a rhombicosadodecahedron.

Source: Wikipedia
Math World