Geometric and asymptotic properties of Brillouin zones in lattices

Each lattice A in W determines a sequence of Brillouin zones Bn, fundamental regions for A bounded by Bragg hyperplanes; for example B, is the Dirichlet region. Basic geometric and topological properties of these zones are established, and we obtain asymptotic estimates (valid for almost all A) for n X(n) = £ ^(') » where L(n) is the number of connected components of the interior of Bn (called Landsberg subzones). Fermi surfaces are also briefly described. 1