45 citations · 57 across the 4 of their papers we have counts for
4 papers
Lattice Delone simplices with super-exponential volume
F. Santos, A. Schuermann, F. Vallentin
In this short note we give a construction of an infinite series of Delone simplices whose relative volume grows super-exponentially with their dimension. This dramatically improves…
Computational Approaches to Lattice Packing and Covering Problems
Achill Schuermann, Frank Vallentin
We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algor…
A Note on Space Tiling Zonotopes
Frank Vallentin
In 1908 Voronoi conjectured that every convex polytope which tiles space face-to-face by translations is affinely equivalent to the Dirichlet-Voronoi polytope of some lattice. In 1…
Some six-dimensional rigid forms
Mathieu Dutour, Frank Vallentin
One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one…