14. A soccer ball should be as round as possible, which suggests using many polygons, each of which is short across. Of course, making a ball with a large number of small pieces requires more sewing. A ball with 92 faces was used for some European soccer competitions: 12 pentagons, 20 hexagons, and 60 triangles (see the accompanying figure), all of them regular polygons. What are the possible vertex types for a polyhedron made up of pentagons, hexagons, and triangles? Explain why the polyhedron underlying this soccer ball is not semiregular.