  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.
