Surface Realization with the Intersection Segment Functional
Stefan Hougardy, Frank H. Lutz, Mariano Zelke · Experimental Mathematics · 2010
Deciding realizability of a given polyhedral map on a (compact, connected) surface belongs to the hard problems in discrete geometry from the theoretical, algorithmic, and practical points of view. In this paper, we present a heuristic algorithm for the realization of simplicial maps, based on the intersection segment functional. This heuristic was used to find geometric realizations in ℝ3 for all vertex-minimal triangulations of the orientable surfaces of genera g = 3 and g = 4. Moreover, for the first time, examples of simplicial polyhedra in ℝ3 of genus 5 with 12 vertices have been obtained.