Surface realization with the intersection edge functional

Details Surface realization with the intersection edge functional Surface realization with the intersection edge functional

2006-08-22

arxiv.org/abs/math/0608538v2

Mathematics

Metric Geometry

22 pages, 11 figures, various minor revisions, to appear in Experimental Mathematics

Scientific paper

10.1016/j.ejc.2008.12.016

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.

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