This page ( and the other football page ) has the truncated icosahedron, otherwise known as the FootBall, which is an Archimedean solid. You can see it on the right of the group above. It is almost as familiar as the cube. Just imagine the pentagons are black and the hexagons white.

It is joined by the Great Rhombicosidodecahedron, because is it similar and also football like. This is the one on the left. It is one of the archimedean solids.

The middle one is a framework that is not an Archimedean solid, but is worth putting here because it is basically a football where the regular pentagons and hexaxons join up by the corners rather than by the sides. It is similar to the football because it has the same number of pentagons and hexagons. It is similar to the great rhombicosidodecahedron because it has the same number of sticks: 180 !!

In this way, it has the same relationship to a football as an icosidodecahedron does to a dodecahedron. It isnt an archimedean solid because not all intersections are identical. Also, the "hexagons" are not exact hexagons. A deformation of this object would be a framework created by arranging 12 pentagrams into the shape of a dodecahedron. Note that there are two ways of doing that, and this way is NOT the same as that which is actually a compound of five cubes.