43 citations · 87 across the 8 of their papers we have counts for
8 papers
Enumerating perfect forms
Achill Schuermann
A positive definite quadratic form is called perfect, if it is uniquely determined by its arithmetical minimum and the integral vectors attaining it. In this self-contained survey…
The isodiametric problem with lattice-point constraints
M. A. Hernandez Cifre, A. Schuermann, F. Vallentin
In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is sh…
Classification of eight dimensional perfect forms
Mathieu Dutour Sikiric, Achill Schuermann, Frank Vallentin
In this paper, we classify the perfect lattices in dimension 8. There are 10916 of them. Our classification heavily relies on exploiting symmetry in polyhedral computations. Here w…
A generalization of Voronoi's reduction theory and its application
Mathieu Dutour Sikiric, Achill Schuermann, Frank Vallentin
We consider Voronoi's reduction theory of positive definite quadratic forms which is based on Delone subdivision. We extend it to forms and Delone subdivisions having a prescribed…
Three-dimensional antipodal and norm-equilateral sets
Achill Schuermann, Konrad Swanepoel
We characterize the three-dimensional spaces admitting at least six or at least seven equidistant points. In particular, we show the existence of norms on admitti…
On packing spheres into containers (about Kepler's finite sphere packing problem)
Achill Schuermann
In an Euclidean -space, the container problem asks to pack equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and $d\…