Cubic Tessellations of the Helicosms

Isabel Hubard; Mark Mixer; Daniel Pellicer; Asia Ivic Weiss

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arXiv · 1505.00191

Cubic Tessellations of the Helicosms

Isabel Hubard·Mark Mixer·Daniel Pellicer·Asia Ivic Weiss

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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.

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BibTeX RIS

Isabel Hubard, Mark Mixer, Daniel Pellicer, Asia Ivic Weiss. 2015-05-01. Cubic Tessellations of the Helicosms. https://arxiv.org/abs/1505.00191

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