2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229110In 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.20 pages, 2 figures, 5 tablesMetric GeometryComputational GeometryInformation TheoryNumber Theory11H56, 11H06, 11B1, 03D15, 52B55, 52B12text