Polyhedral tori with minimal coordinates
Metric Geometry
2007-09-19 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.0709.2794,
title = {Polyhedral tori with minimal coordinates},
author = {Stefan Hougardy and Frank H. Lutz and Mariano Zelke},
journal= {arXiv preprint arXiv:0709.2794},
year = {2007}
}
Comments
5 pages, 4 figures, submitted to Electronic Geometry Models