A Mathematical Tribute to the Soccer Ball
nytimes.com
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.
> The surfaces of nonconvex polyhedra can have various Euler characteristics:
It's strange because the examples use weird faces, but in most (all?) of them it is possible to split the weird faces into a few poligonal faces and get V-E+F=2. For example https://en.wikipedia.org/wiki/Small_stellated_dodecahedron use faces that are stars that intersect other faces and the intersection is not an edge. Replacing each star with 5 triangles the Euler characteristic is 2.