Rotational coherence spectroscopy has been used to measure rotational constants for four isotopomers of the aromatic-aromatic dimer perylene-benzene. Possibilities for the vibrationally averaged dimer geometry have been deduced from the measured values. In the geometries the benzene moiety is close to centrally bound to the perylene and such that its ring plane is parallel or nearly parallel to the plane of the perylene. The geometries are discussed in terms of both the intermolecular forces between the species and the structural results for other aromatic dimers.