  Zeta functions of periodic cubical lattices are explicitly derived by
computing all the eigenvalues of the adjacency operators and their
characteristic polynomials. We introduce cyclotomic-like polynomials to give
factorization of the zeta function in terms of them and count the number of
orbits of the Galois action associated with each cyclotomic-like polynomial to
obtain its further factorization. We also give a necessary and sufficient
condition for such a polynomial to be irreducible and discuss its
irreducibility from this point of view.
