Using the methods developed in a previous paper, we generalize the calculation of the dual amplitude for a nonplanar diagram with a single closed loop to the case with an arbitrary number of "twisted vertices." Just as with the four-point function discussed in the previous paper, we find that, if we write the amplitude M=Σd4ΠM(Π), M(Π) is periodic in Π, the period being given by the sum of the four-momenta of the "twisted vertices." We then show in the general case that the prescription of choosing Σ to range over just one period yields the imaginary part required by perturbative unitarity. We verify that M so defined is dual in three different ways. We show explicitly that our result is equivalent to the Kikkawa-Klein-Sakita-Virasoro (KKSV) prescription; we also prove duality directly from the Bardakci-Ruegg-like form without reference to the KKSV structure; and finally we show that duality is manifest within the operator formalism before the trace is performed.