The complete classification of five-dimensional Dirichlet - Voronoi polyhedra of translational lattices

This paper reports on the full classification of Dirichlet{--}Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110244 affine types ({\it L}-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet{--}Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.     «

This paper reports on the full classification of Dirichlet{--}Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110244 affine types ({\it L}-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet{--}Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181394 contraction types are obtained. The paper gives deta...     »