A Mathematical Tribute to the Soccer Ball(nytimes.com) |
A Mathematical Tribute to the Soccer Ball(nytimes.com) |
(I haven't solved this problem, but I think it is doable.)
V - E + F = 2
where V, E, F are the number of vertices, edges, and faces, respectively.
This holds for any polyhedron (and other shapes have similar equations possibly with a different right hand side) and the left hand side is called the Euler characteristic of the soccer ball (or any polyhedron).
Spoiler warning: the Wikipedia article for the Euler characteristic [0] has a worked out example specifically for the soccer ball.