  We construct explicit examples of weak Hopf algebras (actually face algebras
in the sense of Hayashi) via vacant double groupoids as explained in
\http://arxiv.org/abs/math.QA/0308228. To this end, we first study the Kac
exact sequence for matched pairs of groupoids and show that it can be computed
via group cohomology. Then we describe explicit examples of finite vacant
double groupoids.
