  Up to isomorphism there are six fixed-point free crystallographic groups in
Euclidean Space generated by twists (screw motions). In each case, an
orientable 3-manifold is obtained as the quotient of E3 by such a group. The
cubic tessellation of E3 induces tessellations on each such manifold. These
tessellations of the 3-torus and the didicosm were classified as `equivelar
toroids' and `cubic tessellations of the didicosm' in previous works. This
paper concludes the classification of cubic tessellations on the remaining four
orientable manifolds.
