  The order complex of inclusion poset $PF_n$ of Borel orbit closures in
skew-symmetric matrices is investigated. It is shown that $PF_n$ is an
EL-shellable poset, and furthermore, its order complex triangulates a ball. The
rank-generating function of $PF_n$ is computed and the resulting polynomial is
contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric
matrices over finite fields.
