Surface realization with the intersection edge functional
Metric Geometry
2009-05-13 v2 Combinatorics
Abstract
Deciding realizability of a given polyhedral map on a (compact, connected) surface belongs to the hard problems in discrete geometry, from the theoretical, the algorithmic, and the practical point of view. In this paper, we present a heuristic algorithm for the realization of simplicial maps, based on the intersection edge functional. The heuristic was used to find geometric realizations in R^3 for all vertex-minimal triangulations of the orientable surfaces of genus g=3 and g=4. Moreover, for the first time, examples of simplicial polyhedra in R^3 of genus 5 with 12 vertices were obtained.
Cite
@article{arxiv.math/0608538,
title = {Surface realization with the intersection edge functional},
author = {Stefan Hougardy and Frank H. Lutz and Mariano Zelke},
journal= {arXiv preprint arXiv:math/0608538},
year = {2009}
}
Comments
22 pages, 11 figures, various minor revisions, to appear in Experimental Mathematics