This image was found at bulatov.org, and shows all 92 Johnson solids. As far as i know, this image was created by Vladimir Bulatov.
The Johnson solids are difficult to explain, but I will give it a shot! First, imagine that you are considering ALL possible polyhedra which are (A) convex, and (B) have only regular, convex polygons as faces. This is a large set of polyhedra. Now, remove from this set the five Platonic solids, the thirteen Archimedean solids, and all of the prisms and antiprisms (see my last four posts for descriptions of these sets, if needed). In the mid-1960s, a mathematician named Norman Johnson examined this situation, and found exactly 92 polyhedra which are left after these four “subtractions.” He also named all 92 of them (and they have some real tongue-twister names, such as “metabidiminished rhombicosidodecahedron”).
This work was completed in 1966. Three years later, in 1969, another mathematician (Victor Zalgaller) proved that Johnson’s list of 92 was, in fact, complete. The proof for this is NOT simple.
More information about the Johnson solids: http://en.wikipedia.org/wiki/Johnson_solids