Single-crystal X-ray structure determinations of Ce4I6CN and disordered Ce6I9C2N phases are described together with electron-microscopy studies of Ce6I9C2N and Y6I9C2N. Ce4I6CN crystallizes in the tetragonal space group P42/mnm with a = 13.877(2) Å, c = 9.665(2) Å. Compounds β′-Ce6I9C2N and β″-Ce6I9C2N crystallize in space group P6/m with a = 41.774(6) Å, c = 13.719(3) Å and a = 20.958(3) Å, c = 13.793(3) Å, respectively. The main structural feature of these compounds are rods of RE6C2 octahedra and RE4N tetrahedra (RE = lanthanide) interconnected in different sequences. These rods are linked into Kagomé-type frameworks with additional rods located in the centres of thehexagonal channels. The disorder patterns for these additional rods can be rationalized in terms of nearest-neighbour interactions.