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- Martin Henk, John C. Wood
- 2006

spherical and hyperbolic space. It is divided into two equal-sized parts: the first is devoted to the two-dimensional case, where much more is known than in the n-dimensional setting, which is… (More)

- Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler
- Handbook of Discrete and Computational Geometry…
- 2004

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical… (More)

- Ulrich Betke, Martin Henk
- Comput. Geom.
- 2000

Based on Minkowski’s work on critical lattices of 3-dimensional convex bodies we present an efficient algorithm for computing the density of a densest lattice packing of an arbitrary 3-polytope. As… (More)

- Martin Grötschel, Martin Henk
- Discrete & Computational Geometry
- 2003

A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every ^-dimensional polyhedron admits a representation as… (More)

- Ulrich Betke, Martin Henk, Jörg M. Wills
- Discrete & Computational Geometry
- 1993

We show analogues of Minkowski’s theorem on successive minima, where the volume is replaced by the lattice point enumerator. We further give analogous results to some recent theorems by Kannan and… (More)

- Martin Henk
- 2008

We show that for every lattice packing of n-dimensional spheres there exists an (n/ log2(n))-dimensional affine plane which does not meet any of the spheres in their interior, provided n is large… (More)

- Ulrich Betke, Martin Henk
- 2006

Hadwiger showed by computing the intrinsic volumes of a regular simplex that a rectangular simplex is a counterexample to Wills’s conjecture for the relation between the lattice point enumerator and… (More)

- Martin Henk
- Inf. Process. Lett.
- 1997

K is a centrally symmetric convex body with nonempty interior and fK(·) is also called the distance function of K because fK(x) = min{ρ ∈ R≥0 : x ∈ ρK}. The Euclidean norm is denoted by fB(·), where… (More)

- Christian Bey, Martin Henk, Jörg M. Wills
- Discrete & Computational Geometry
- 2007

We determine lattice polytopes of smallest volume with a given number of interior lattice points. We show that the Ehrhart polynomials of those with one interior lattice point have largest roots with… (More)

- Ulrich Betke, Martin Henk
- Discrete & Computational Geometry
- 1993

It is a well known fact that for every polynomial time algorithm which gives an upper bound V (K) and a lower bound V (K) for the volume of a convex set K ⊂ E, the ratio V (K)/V (K) is at least (cd/… (More)