#### Filter Results:

- Full text PDF available (6)

#### Publication Year

1967

2010

- This year (0)
- Last 5 years (0)
- Last 10 years (4)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

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 difference of this bipartition is a lower bound for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile [Adv. Math.… (More)

- Thilo Rörig, Nikolaus Witte, Günter M. Ziegler
- Discrete & Computational Geometry
- 2009

There are d-dimensional zonotopes with n zones for which a 2-dimensional central section has Ω(nd−1) vertices. For d = 3 this was known, with examples provided by the “Ukrainian easter eggs” by Eppstein et al. Our result is asymptotically optimal for all fixed d ≥ 2.

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.

- Nikolaus Witte, W W Kryshanowskaja, E I Steshenskaya
- Zeitschrift für Alternsforschung
- 1967

- Nikolaus Witte
- 2007

Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d ≤ 4 every closed oriented PL… (More)

- Ewgenij Gawrilow, Michael Joswig, Thilo Rörig, Nikolaus Witte
- Computat. and Visualiz. in Science
- 2010

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 combinatorics such as tight spans of finite metric spaces and tropical polytopes. In all our cases we arrive at specific, geometrically motivated, graph drawing problems. The… (More)

The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects.

- ‹
- 1
- ›