We introduce a large class of transformations allowing rearrangements
of the fullerene surface. We call this set of rearrangements generaliz
ed Stone-Wales transformations (gSW) because the well-known Stone-Wale
s (or pyracylene) flip may be seen as the simplest representative of t
he novel gSW family. The interconversion between the two C-28 fulleren
e isomers is presented as a simple example of gSW application. Further
examples involving the complete generation of C-60 and C-70 isomer sp
aces are provided. In both cases, just one fullerene molecule is used
as seed data. Some considerations on gSW energetics are also reported.