Mathieu Dutour Sikirić

Geometry of Numbers

A lattice L is a discrete subgroup set of the Euclidean space. In a lattice L an empty sphere is a sphere containing no lattice points in its interior and containing n+1 affinely independent points on its surface. A Delaunay polytope is the convex hull of the points on the surface of an empty sphere.

Delaunay polytopes form a tesselation dual to the Voronoi partition, which has a lot of uses in computational geometry and physics. We design specific algorithm for enumerating the Delaunay polytopes under symmetry.