It seems that mostly either 26 or 32 equal-size polygons are used to cover a spherical soccer ball. What other configurations are possible?
There are an infinite number of ways to cover a soccer ball, if you're allowed to use "biangles", polygons with two sides and two vertices. Draw a line from the ball's north pole to its south pole. Repeat this process any number of times. Now you have a "beach ball" pattern, with however many slices you desire, all of equal size.
If you don't allow biangles, but you do allow non-regular polygons, take the above pattern and draw a line around the equator; now you have any number of 90-90-?? triangles.
Most of the possible solutions would be found in the collection of Platonic or Archimedean solids.
The platonic fit the description of same size faces: http://www.korthalsaltes.com/cuadros.php?type=p
In that case the options are 4 6 8 12 or 20. (note: some of them are highly unenjoyable to play with).
The Archimedean solids might offer a better fit: http://www.korthalsaltes.com/cuadros.php?type=a (includes the standard truncated icosahedron which is commonly used)
However, none of them have solutions with equal size polygons, they each consist of a combination of at least two 'regular' polygons.
Once again, with most of these I wouldn't enjoy playing around.
I think the Catalan solids would qualify as well. The faces are all equal polygon, although the polygons themselves don't have equal sides. Biggest would probably be the Pentagonal Hexecontahedron http://en.wikipedia.org/wiki/Pentagonal_hexecontahedron