THE discovery of conductivity 1 in A(x)C60 (where A represents an alkali metal) and superconductivity 2 in K(x)C60 has been followed by reports of superconductivity in other alkali-metal-doped fullerides with transition temperatures as high as 33 K (ref. 3). Elucidation of phase diagrams and understanding the relationship between structure and superconducting properties is essential to a detailed understanding of superconductivity in these systems. So far, structural data have been reported only for the non-conducting, intercalated body-centred cubic (b.c.c.) structures A6C60 (where A is K or Cs; ref. 4), a body-centred tetragonal structure for A4C60 (where A is K, Rb, Cs; ref. 5) and the superconducting, intercalated face-centred cubic (f.c.c.) material K3C60 (ref. 6). Here we report the preparation of a series of single-phase, isostructural f.c.c. superconductors with composition A3C60 (where A is K, Rb, Cs or a mixture of these), and show that T(c) increases monotonically with the size of the unit cell. Extended Huckel band-structure calculations also show a monotonic increase in the density of states at the Fermi level, N(E(F)), with lattice parameter. The primary implication of these results is that all A3C60 superconductors have the same structure and that changes in T(c) can be accounted for by changes in N(E(F)).