35 citations · 75 across the 13 of their papers we have counts for
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math.MG2007★ 2 cited
Polyhedral tori with minimal coordinates
Stefan Hougardy, Frank H. Lutz, Mariano Zelke
We give explicit realizations with small integer coordinates for all triangulated tori with up to 12 vertices. In particular, we provide coordinate-minimal realizations in general…
math.MG2006★ 35 cited
Surface realization with the intersection edge functional
Stefan Hougardy, Frank H. Lutz, Mariano Zelke
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…
math.MG2005★ 4 cited
Polyhedra of genus 2 with 10 vertices and minimal coordinates
Stefan Hougardy, Frank H. Lutz, Mariano Zelke
We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.