The geometric structure of the Rh8+ cation is investigated using a combination of far-infrared multiple photon dissociation spectroscopy and density functional theory (DFT) calculations. The energetic ordering of the different structural motifs is found to depend sensitively on the choice of pure or hybrid exchange functionals. Comparison of experimental and calculated spectra suggests the cluster to have a close-packed, bicapped octahedral structure, in contrast to recent predictions of a cubic structure for the neutral cluster. Our findings demonstrate the importance of including some exact exchange contributions in the DFT calculations, via hybrid functionals, when applied to rhodium clusters, and cast doubt on the application of pure functionals for late transition metal clusters in general.