  One can always decompose Dirichlet-Voronoi polytopes of lattices
non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid
lattices. In this report we show how one can enumerate all rigid positive
semidefinite quadratic forms (and thereby rigid lattices) of a given dimension
d. By this method we found all rigid positive semidefinite quadratic forms for
d = 5 confirming the list of 7 rigid lattices by Baranovskii and Grishukhin.
Furthermore, we found out that for d <= 5 the adjacency graph of primitive
L-type domains is an infinite tree on which GL_d(Z) acts. On the other hand, we
demonstrate that in d = 6 we face a combinatorial explosion.
