Polyhedral tori with minimal coordinates

Details Polyhedral tori with minimal coordinates Polyhedral tori with minimal coordinates

2007-09-18

arxiv.org/abs/0709.2794v1

Mathematics

Metric Geometry

5 pages, 4 figures, submitted to Electronic Geometry Models

Scientific paper

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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