  In a companion manuscript, we introduce a stratification of intersections of
a top dimensional real Bruhat cells with another arbitrary cell. This
intersection is naturally identified with a subset of the lower triangular
group: these subsets are labeled by elements of a finite group, the lift to the
spin group of the intersection of a Coxeter group with the special orthogonal
group. The stratification allows us to determine the homotopy type of the
intersection. In this work we give more examples, particularly detailing the
computation of the intersection of two open Bruhat cells in general position
for $n=4$. It turns out that all connected components are contractible.
