2 citations · 3 across the 6 of their papers we have counts for
6 papers
Drawing polytopal graphs with polymake
Ewgenij Gawrilow, Michael Joswig, Thilo Rörig +1
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric…
Zonotopes With Large 2D Cuts
Thilo Rörig, Nikolaus Witte, Günter M. Ziegler
There are d-dimensional zonotopes with n zones for which a 2-dimensional central section has Ω(n^{d-1}) vertices. For d=3 this was known, with examples provided by the "Ukrainian e…
Constructing Combinatorial 4-Manifolds
Nikolaus Witte
Every closed oriented PL 4-manifold is a branched cover of the 4-sphere branched over a PL-surface with finitely many singularities by Piergallini [Topology 34(3):497-508, 1995]. T…
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.
Constructing Simplicial Branched Covers
Nikolaus Witte
Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets a…
Products of Foldable Triangulations
Michael Joswig, Nikolaus Witte
Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. The (weighted) size d…