The truncated icosahedron has 32 faces ,it contains twenty hexagonal faces ,and twelve pentagonal faces is the Archimedea   solid  ,and it is uniform polyhedron   and Wenninger model.

         It is the shape used in the construction of soccer balls, and it was also the configuration of the lenses used for focusing the explosive shock waves of the detonators in the Fat Man atomic bomb (Rhodes 1996, p. 195). The truncated icosahedron has 60 vertices, and is also the   structure of pure carbon known as buckyballs (a.k.a. fullerenes ).

       The surface area  of the solid is

The volumn  of the solid is