The classical soccer ball, introduced at the world championship 1970, consists of pentagonal and hexagonal leather pieces sewn together along the edges, see picture. Each hexagon is surrounded by alternatively pentagons and hexagons, and each pentagon is surrounded by only hexagons. At each corner exactly three leather pieces meet.

Show that with this pattern there is only one possible size of the ball, counted as the number of pentagons and hexagons. Also find these numbers.