Only soccer ball or dodecahedron.

Clearly 3 hexagons can not meet at one vertex. Thus we have only 3 choices for one vertex:

• 3 pentagons
• 2 pentagons + 1 hexagon
• 1 pentagons + 2 hexagon

Now

• Once you have a vertex of the first type you have a regular dodecahedron.
• If you have a vertex of the second type then you will get one hexagon surrounded by pentagons. Then it is easy to see that you can not continue.
• For the third type you will get a soccer ball or "truncated icosahedron" as some people call it :)

Only soccer ball or dodecahedron.

Clearly 3 hexagons can not meet at one vertex. Thus we have only 3 choices for one vertex:

• 3 pentagons
• 2 pentagons + 1 hexagon
• 1 pentagons + 2 hexagon

Note that if $[pq]$ is an edge then $p$ has the same type as $q$ (the type is determined by angle at $[pq]$). Thus the polyhedron is completely determined by one vertex. Further:

• Once you have a vertex of the first type you have a regular dodecahedron.
• If you have a vertex of the second type then you will get one hexagon surrounded by pentagons. Then it is easy to see that you can not continue.
• For the third type you will get a soccer ball or "truncated icosahedron" as some people call it :)