The room-temperature crystal structures of Ba6Mn4MO15 (M Zn, Cu) have been refined using X-ray and neutron powder diffraction data simultaneously. Ba6Mn4ZnO15 is isostructural with Ba6Ni5O15 and contains transition metals in chains of oxide polyhedra (trigonal prisms and octahedra); neighboring chains are separated from each other by the Ba atoms. Zn and Mn occupy the trigonal prismatic site in equal concentrations, with the remaining Zn and Mn partially ordered over the two crystallographically distinct octahedral sites. The neutron diffraction data show Ba6Mn4CuO15 to adopt a very similar structure but reveal that Cu is displaced from the center of the trigonal prism to give pseudo-square-planar coordination. A neutron diffraction experiment performed at 1.7 K showed additional intensity due to long-range magnetic order on the octahedral sites, and this has been modeled using an unusual magnetic structure in which the antiferromagnetic superexchange within the highly frustrated crystal structure leads to a rotation of 120 degrees between spins in neighboring chains. The magnetic moments refined to 0.16(2) and 0.12(3) mu(B) per octahedral site in the Cu and Zn compounds, respectively. The magnetic susceptibility of Ba6Mn4CuO15 is consistent with the trigonal prismatic Cu remaining paramagnetic in the range 5 less than or equal to T/K less than or equal to 300, in which case the contribution to the susceptibility from the octahedrally coordinated Mn is qualitatively similar to the observed susceptibility of Ba6Mn4ZnO15, showing a broad maximum (90(5) K for M = Cu, 45(5) K for M = Zn) indicative of 1-dimensional ordering. In neither compound is it possible to identify the Neel temperature, although the susceptibility of Ba6Mn4CuO15 suggests that the Cu spins in trigonal prismatic coordination freeze at 5 K, and it is likely that this coincides with the onset of long-range magnetic ordering on the octahedral sites.