decompositions of graphs have a number of applications, for example, programming for multiple processor computers. in particular, this makes decompositions of high dimensional cubes into hamiltonian cycles of interest. these decompositions are most easily approached by looking at decompositions of more general cartesian products. for the undirected case, these decompositions are fairly well understood, but i want to present a new way of looking at these constructions. this new outlook allows one to solve the directed case as well.