  Following Gromov, the coboundary expansion of building-like complexes is
studied. In particular, it is shown that for any $n \geq 1$, there exists a
constant $\epsilon(n)>0$ such that for any $0 \leq k <n$ the $k$-th coboundary
expansion constant of any $n$-dimensional spherical building is at least
$\epsilon(n)$.
