Cubic Tessellations of the Helicosms (1505.00191v1)

Abstract: 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' andcubic tessellations of the didicosm' in previous works. This paper concludes the classification of cubic tessellations on the remaining four orientable manifolds.