We report on a survey of the potential energy surface for the 13-molecule benzene cluster, (C6H6)(13), bound by an atom-atom intermolecular potential developed from first principles. The potential, which has an anisotropic repulsion term, is found to support distinct pairs of structures of C-3, C-i, and S-6 symmetry as low-lying minima, including a C-3 global minimum. The organisation of the low-lying region of the potential energy surface suggests that one of the S-6 structures is likely to act as a kinetic trap, hindering efficient relaxation to the global minimum, in agreement with the hypothesis that two isomers coexist in this system, suggested by spectroscopic experiments.