  Recent studies have demonstrated that {\em secondary} non-Gaussianity induced
by gravity will be detected with a high signal-to-noise (S/N) by future and
even by on-going weak lensing surveys. One way to characterise such
non-Gaussianity is through the detection of a non-zero three-point correlation
function of the lensing convergence field, or of its harmonic transform, the
bispectrum. A recent study analysed the properties of the squeezed
configuration of the bispectrum, when two wavenumbers are much larger than the
third one. We extend this work by estimating the amplitude of the (reduced)
bispectrum in four generic configurations, i.e., {\em squeezed, equilateral,
isosceles} and {\em folded}, and for four different source redshifts
$z_s=0.5,1.0,1.5,2.0$, by using an ensemble of all-sky high-resolution
simulations. We compare these results against theoretical predictions. We find
that, while the theoretical expectations based on widely used fitting functions
can predict the general trends of the reduced bispectra, a more accurate
theoretical modelling will be required to analyse the next generation of
all-sky weak lensing surveys. The disagreement is particularly pronounced in
the squeezed limit.
