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math.MG2004★ 45 cited
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…
math.MG2004★ 5 cited
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…
math.MG2004★ 6 cited
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…