Random walks in polytype structures

It is shown that the total number of walks, starting and ending at the same point and having the same number of steps, is the same for all polytype structures in the fcc, hcp series and in the zincblende, wurtzite series and is independent of the starting point. This result is proved by showing that the eigenvalues of a simple Hamiltonian are the same within the two series considered. A relation is found between random walks in the two series of structures that is useful in extending currently available tables of random walks for the zincblende structure.