[ddfbzyds] sorted Goldberg polyhedra

Goldberg polyhedra are the dual of geodesic polyhedra.  here are the first few Goldberg polyhedra of icosahedral symmetry, sorted by number of faces.  all these Goldberg polyhedra have 12 regular pentagonal faces and the rest are hexagons, usually not regular.  (other than truncated icosahedron, are there any regular hexagons?)

12 faces: GP(1,0) regular dodecahedron
32 faces: GP(1,1) truncated icosahedron
42 faces: GP(2,0) chamfered dodecahedron
72 faces: GP(2,1)
92 faces: GP(3,0)
122 faces: GP(2,2)
132 faces: GP(3,1)
162 faces: GP(4,0)
192 faces: GP(3,2)
212 faces: GP(4,1)
252 faces: GP(5,0)
272 faces: GP(3,3)
282 faces: GP(4,2)
312 faces: GP(5,1)
362 faces: GP(6,0)
372 faces: GP(4,3)
392 faces: GP(5,2)
432 faces: GP(6,1)
482 faces: GP(4,4)
492 faces: GP(5,3)
492 faces: GP(7,0)

we stopped at the first instance where the number of faces does not uniquely identify the polyhedron.

number of faces of GP(m,n) = 2 + 10*((m+n)^2 - m*n), according to Wikipedia.  what is the growth rate of the sorted sequence?

do Goldberg polyhedra have freedom to adjust location of face centers?  as spherical polyhedra, can the faces be adjusted while keeping the same topology so that the faces are more uniform in area?  perhaps move the face centers then Voronoi.