MathDB

A soccer ball is usually made from a polyhedral fugure model, with two types of faces, hexagons and pentagons, and in every vertex incide three faces - two hexagons and one pentagon.
We call a polyhedron soccer-ball if it is similar to the traditional soccer ball, in the following sense: its faces are

m

-gons or

n

-gons,

m \not= n

, and in every vertex incide three faces, two of them being

m

-gons and the other one being an

n

-gon.
[list='i'] [*] Show that

m

needs to be even. [*] Find all soccer-ball polyhedra.

Problem Statement