The proposed all-optical 2-D switching networks are (i) M ×N -gon prism switches (M ¿2; N¿3) and (ii) 3-D grids of any geometry N ¿3. For the routing we assume (1) the projection of the spatial architectures onto plane graphs (2) the embedding of the latter guest graphs into (in)complete host hypercubes (N = 4) and generally, into N -cube networks (N ¿3) and (3) routing by means of the cube algorithms of the host. By the embedding mainly faulty cubes (synonyms: injured cubes, incomplete cubes) arise which complicate the routing and analysis. The application of N -cube networks (i) extend the hypercube principles to any N ¿3 (ii) increase the number of plane host graphs and (iii) reduce the incompleteness of the host cubes. Several di erent embeddings of the intersection graphs (IGs) of 2-D switching networks and several di erent routings are explained for N = 4 and 6 by various examples. By the expansion of the grids (enlargement) internal waveguides (WGs) and internal switches are introduced which interact with the switches of the original 3-D grid without increasing the number of stages (NS). The embeddings by expansion apply to interconnection networks whereas dilation-2 embeddings (dilation ≡ distance of the nearest-neighbour nodes of the guest graph at the host) are rather suitable for the emulation of algorithms. Concepts for fault-tolerant routing and algorithm mapping are brie y explained.