Can you compute the ratio of shapes on a soccer ball?

The traditional shape of a soccer ball is a combination of hexagons and pentagons. It is an example of an Archimedean solid, which means that although there are different shapes, the vertices are indistinguishable. At each vertex, two hexagons and one pentagon come together. It may seem at first that the ratio of shapes is two to one, but that is not quite right. Can you find the ratio?

Extra credit – Using Euler’s equation and a little algebra, it is possible to determine the number hexagons and pentagons. For any shape that covers the surface of a sphere, F – E + V = 2. F is the number of faces, i.e., the number of hexagons plus pentagons. E is the number of edges and V is the number of vertices.