  The third-rank tensor of the static spin Hall conductivity is investigated
for two-dimensional (2D) topological insulators by electronic structure
calculations. Its seeming quantization is numerically demonstrated for highly
symmetric systems independent of the gap size. 2D crystals with hexagonal and
square Bravais lattice show similar effects, while true rectangular
translational symmetry yields conductivity values much below the quantum
$e^2/h$. Field-induced lifting the inversion symmetry does not influence the
quantum spin Hall state up to band inversion but the conductivity quantization.
Weak symmetry-conserving biaxial but also uniaxial strain has a minor influence
as long as inverted gaps dictate the topological character. The results are
discussed in terms of the atomic geometry and the Rashba contribution to the
spin-orbit interaction (SOI). Translational and point-group symmetry as well as
SOI rule the deviation from the quantization of the spin Hall conductance.
