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arXiv · 0709.2794

Polyhedral tori with minimal coordinates

Stefan Hougardy·Frank H. Lutz·Mariano Zelke
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Abstract

We give explicit realizations with small integer coordinates for all triangulated tori with up to 12 vertices. In particular, we provide coordinate-minimal realizations in general position for all triangulations of the torus with 7, 8, 9, and 10 vertices. For the unique 7-vertex triangulation of the torus we show that all corresponding 72 oriented matroids are realizable in the 6x6x6-cube. Moreover, we present polyhedral tori with 8 vertices in the 2x2x2-cube, general position realizations of triangulated tori with 8 vertices in the 2x2x3-cuboid as well as polyhedral tori with 9 and 10 vertices in the 1x2x2-cuboid.

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Stefan Hougardy, Frank H. Lutz, Mariano Zelke. 2007-09-18. Polyhedral tori with minimal coordinates. https://arxiv.org/abs/0709.2794

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