  It is shown that the hopping of a single excitation on certain triangular
spin lattices with non-uniform couplings and local magnetic fields can be
described as the projections of quantum walks on graphs of the ordered Hamming
scheme of depth 2. For some values of the parameters the models exhibit perfect
state transfer between two summits of the lattice. Fractional revival is also
observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik
type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2
give the overlaps between the energy eigenstates and the occupational basis
vectors.
