English

Cubic Tessellations of the Helicosms

Geometric Topology 2015-05-04 v1

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' and `cubic tessellations of the didicosm' in previous works. This paper concludes the classification of cubic tessellations on the remaining four orientable manifolds.

Keywords

Cite

@article{arxiv.1505.00191,
  title  = {Cubic Tessellations of the Helicosms},
  author = {Isabel Hubard and Mark Mixer and Daniel Pellicer and Asia Ivic Weiss},
  journal= {arXiv preprint arXiv:1505.00191},
  year   = {2015}
}