35 citations · 127 across the 21 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.MG2007★ 2 cited
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.
math.MG2007★ 2 cited
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.