We calculate electrostatic multipole moments of C60 up to l=18 using the quantum-mechanical charge distribution with icosahedral symmetry obtained from ab initio calculations. It is found that the second nonzero moment (l=10) is comparable to the first nonzero moment (l=6). The values of several low-order multipole moments are almost 10 times smaller than those found from the charge distribution of recently proposed potential models and thus the actual Coulomb interaction between C60 molecules is much smaller than previously predicted. Much better agreement with calculated multipoles is obtained from a model which introduces point charges at the center of hexagonal and pentagonal plaquettes, following the physical arguments of David et al. [Nature 353, 147 (1991)]. We show that a multipole expansion including only l=6 and 10 moments can predict the potential due to a C60 molecule at distances R≥2R0 within an error of about 5%, where R0 is the radius of the C60 molecule. At distances less than R<3/2R0 the multipole expansion is qualitatively incorrect even if one includes the terms up to l=18, indicating the importance of short-range quantum effects at these distances. The Coulomb interaction we obtain predicts two nearly degenerate, locally stable configurations for solid C60: (1) a metastable structure with Pa3 symmetry and setting angle φ=23.3°, close to experimentally observed value, and (2) a global minimum with the Pa3 structure but a setting angle φ=93.6°. We give physical arguments for expecting two such configurations and give a qualitative explanation for their near degeneracy. We conclude that a satisfactory intermolecular potential requires a first-principles calculation of the quantum-mechanical short-range repulsive interactions.