One metal atom surrounded by its 12 nearest neighbors is considered for both D3d (face-centered cubic-like) and D3h (hexagonal close-packed-like) geometries. For Al and Be, the neutral cluster and the positive and negative ions are considered for idealized (all bonds equal) and distorted geometries. The D3d geometry is found to be the lowest for Be13, while the D3h geometry is lower for Al13. This is the reverse of what is expected based upon the bulk metal structures, Be(hcp) and Al(fcc). Al13 is found to have only small distortions, while Be13 shows large distortions for both the D3d and D3h geometries. The ions have geometries which are similar to those found for the neutral systems. Both all-electron and effective core potential calculations were carried out on the X13 clusters; the agreement is very good. © 1986 American Institute of Physics.