Single crystals of two new barium rhodates were grown from a molten potassium carbonate flux. The new rhodates, Ba11Rh10O30 and Ba32Rh29O87, are structurally related to the 2H-hexagonal perovskite structure and are characterized by pseudo one-dimensional chains of alternating face-sharing trigonal prisms and octahedra. The structures of Ba11Rh10O30 and Ba32Rh29O87 were solved using the 4D superspace group approach in Jana2000. Ba11Rh10O30, with a repeat of nine RhO6 octahedra followed by one RhO6 trigonal prism, contains the longest chain sequence of face-sharing octahedra known for this 2H-perovskite related family of oxides. A structural analysis of these two compounds revealed clear trends in metal-metal distances and octahedral heights not previously identified for this family of oxides. The application of these trends toward the structure of the all-octahedra-containing end member of the structural series, the hypothetical 2H-BaRhO3, enabled a prediction of its rhodium-rhodium distance, octahedral height, and lattice parameters.