We located the geometric structures of (Au 20 ) N (N=2–40) clusters using the basin-hopping method and multiple-center Lennard-Jones model potential. Some magic number structures have been observed, among which (Au 20 ) 5 is a close-shell five-membered ring, (Au 20 ) 20 is a hollow-cage, and (Au 20 ) 35 is a double-cage in which the two cages share a five-membered ring. Moreover, the building-up principle of (Au 20 ) N clusters is significantly different from that of the other molecular or atomic clusters. The orientational effect on Au 20 –Au 20 potential is much greater compared to that on C 60 –C 60 potential.