Large single crystals of oxygen-deficient Sr6Co5O15-delta compounds, i.e., Sr6Co5O14.70 and Sr6Co4.9Ni0.1O14.36, were obtained by using K2CO3 flux in the presence of additives of transition metal oxides. The single-crystal structure determination shows that the structures of Sr6Co5O14.70 and Sr6Co4.9Ni0.1O14.36 crystallize in the space group R (3) over bar and can be described as one-dimensional face-sharing CoO3 polyhedral chains and Sr cation chains. Unlike the other known 2H-perovskite-related oxides in which the polyhedral chains consist of octahedra (Oh) and trigonal prism (TP), the structure of Sr6Co5O14.70 and Sr6Co4.9Ni0.1O14.36 contain Oh and intermediate polyhedra (IP) and can be attributed to a general structure formula A(6)A'2B3O15-delta, which is closely related to the known A(6)A'B4O15 phases by shifting of a B atom and the O-3 triangle along the c axis. Further study on O3 reveals that this oxygen position splits into two independent positions, corresponding to polyhedral geometry of IP and TP, respectively. Therefore, the polyhedral chain in the structure should be more precisely described as a random composite of the 4Oh + TP and 3Oh + 2IP. This model is used to interpret the magnetic properties, although not quantitatively. The 4-D structure analysis was also conducted for both Sr6Co5O14.70 and Sr6Co4.9Ni0.1O14.36 with a commensurate modulated structure in a 4-D superspace group, R (3) over barm(00 gamma)0s, gamma = p/k = 3/5. By considering the same 4-D superspace group R (3) over barm(00 gamma)0s but different t-phases, one can understand the structure relationship between Sr6Co5O14.70 and Sr6Rh5O15.