The complete structural characterization of the hexagonal cobaltite BaMn0.4Co0.6O2.83 has been performedby combining high-resolution transmission electron microscopy and electron and neutron diffraction.The structure is closely related to the 12H (cc'chhh)2 with oxygen deficient cubic c'-BaO2 layers. Thisframework forms a laminar structure in which tetramers of face-sharing octahedra occupied by manganeseand cobalt are connected by corners to two tetrahedral layers mostly occupied by cobalt. A magneticstudy shows only the presence of short-range magnetic interactions indicating that there are no interactionsbetween the tetramers through the tetrahedral layers, thus impeding the three-dimensional magnetic orderingof the system. A spin-glass-like state was found to be compatible with the observed phenomenology.