by Mathieu Dutour Sikiric and Achill Schürmann and Frank Vallentin.
Series: 2008-19, Preprints
In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a \sharpp-hard problem. On the other hand we describe an algorithm for this problem which is especially suited for low dimensional (say dimensions at most $12$) and for highly-symmetric lattices. We use our implementation, which drastically outperforms those of current computer algebra systems, to find the vertices of Voronoi cells and quantizer constants of some prominent lattices.
lattice, Voronoi cell, Delone cell, covering radius, quantizer constant, lattice isomorphism problem, zonotope