The two cobalt hexagonal perovskites 6H-Ba6Co6F0.93O16 and 10H-Ba5Co5F0.77O12.88 were prepared, and their structures were examined by X-ray and neutron diffraction and by F-19 solid state NMR spectroscopy. The magnetic and transport properties of these compounds were probed by magnetic susceptibility and electrical resistivity measurements, and their electronic structures by density functional and tight-binding calculations. The [BaOF1-x] layers of these compounds create corner-sharing tetrahedral Co2O7 dimers at the interface between their face-sharing octahedral oligomers. Our density functional calculations leads to an unambiguous charge distribution model, which assigns high-spin Co3+ ions for the tetrahedral sites and low-spin Co3+/Co4+ ions for the octahedral sites, and this model should be valid for the parent BaCoO3-delta and the related oxychlorides and oxybromides as well. The F- vacancies in the [BaOF1-x] layers cause a strong distortion in the tetrahedral dimer Co2O7, which in turn affects the spin orientation of the high-spin Co3+ ions of the CoO4 tetrahedra, i.e., parallel to the c-direction in Ba6Co6F1-xO16-delta but perpendicular to the c-direction in Ba5Co5F1-xO13-delta. This difference in the spin orientations is related to the d-states of the distorted Coal tetrahedra with high-spin Co3+ (d(6)) ion on the basis of tight binding calculations and spin-orbit coupling as perturbation.