  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 #P-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.
