The complete structural characterization of the hexagonal cobaltite BaMn0.4Co0.6O2.83has been performed by combining high-resolution transmission electron microscopy and electron and neutron diffraction. The structure is closely related to the 12H (cc‘chhh)2with oxygen deficient cubic c‘-BaO2layers. This framework forms a laminar structure in which tetramers of face-sharing octahedra occupied by manganese and cobalt are connected by corners to two tetrahedral layers mostly occupied by cobalt. A magnetic study shows only the presence of short-range magnetic interactions indicating that there are no interactions between the tetramers through the tetrahedral layers, thus impeding the three-dimensional magnetic ordering of the system. A spin-glass-like state was found to be compatible with the observed phenomenology. [ABSTRACT FROM AUTHOR]