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2010 Surface Realization with the Intersection Segment Functional
Stefan Hougardy, Frank H. Lutz, Mariano Zelke
Experiment. Math. 19(1): 79-92 (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 ${\mathbb R}^3$ 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 ${\mathbb R}^3$ of genus 5 with 12 vertices have been obtained.


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Stefan Hougardy. Frank H. Lutz. Mariano Zelke. "Surface Realization with the Intersection Segment Functional." Experiment. Math. 19 (1) 79 - 92, 2010.


Published: 2010
First available in Project Euclid: 12 March 2010

zbMATH: 1191.52010
MathSciNet: MR2649986

Primary: 52B70 , 57Q15

Keywords: intersection segment functional , polyhedral realization , triangulated surface

Rights: Copyright © 2010 A K Peters, Ltd.

Vol.19 • No. 1 • 2010
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