Imprimitive distance-regular graphs and projective planes

We investigate a class of (imprimitive) covering graphs Γ of complete bipartite graphs K_k,k and show that they are in one-to-one correspondence with triples (P, l, P), where P is a projective plane of order k and (l, P) is a distinguished flag of P. If Γ is distance-transitive, then P ? l is a self-dual rank three translation plane and may be coordinatised by a semifield.