35 citations · 127 across the 21 of their papers we have counts for
6 papers · 1 filter
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…
Knotted Polyhedral Tori
Frank H. Lutz, Nikolaus Witte
For every knot K with stick number k there is a knotted polyhedral torus of knot type K with 3k vertices. We prove that at least 3k-2 vertices are necessary.
A Small Polyhedral Z-Acyclic 2-Complex in R4
Frank H. Lutz, Günter M. Ziegler
We present a small 4-dimensional polyhedral realization of a 2-dimensional Z-acyclic but non-contractible simplicial complex.
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…
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.
Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres
Frank H. Lutz
The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally sy…