On the orthogonal projections of Dirichlet-Voronoi cells of lattices (Q717848)

The parallelotope is a convex polytope which fills the space facet to facet by its translation copies without intersecting by inner points. In this paper the authors give a condition when the orthogonal projections of the \(n\)-dimensional Dirichlet-Voronoi cells of \(n\)-lattices (which are special types of the parallelotopes) are \((n-1)\)-dimensional Dirichlet-Voronoi cells. They show certain applications for the Dirichlet-Voronoi cells of the lattices \(Z_{n}, A_{n}\) and \(D_{n}\).