Can I polyhedron been made up of hexagons?

The “truncated icosahedron” (the traditional soccer ball pattern) is made up of 32 panels, 20 of which are hexagons, and 12 of which are pentagons. If this meets your needs, this is the most common example. I believe it is impossible to make a polyhedron with just hexagonal faces. read more

Although it is not proven here, no such polyhedron can be constructed with h=1. But for any other number of hexagons a polyhedron made up of only hexagons and 12 pentagons exists. If h=1 is forbidden then from the above equation v=22 is forbidden. Thus there is no polyhedron composed only of hexagons and pentagons with 22 vertices. read more