  Let $I\subset K[x_1,\ldots,x_n]$ be a zero-dimensional monomial ideal, and
$\Delta(I)$ be the simplicial complex whose Stanley--Reisner ideal is the
polarization of $I$. It follows from a result of Soleyman Jahan that
$\Delta(I)$ is shellable. We give a new short proof of this fact by providing
an explicit shelling. Moreover, we show that $\Delta(I)$ is even vertex
decomposable. The ideal $L(I)$, which is defined to be the Stanley--Reisner
ideal of the Alexander dual of $\Delta(I)$, has a linear resolution which is
cellular and supported on a regular CW-complex. All powers of $L(I)$ have a
linear resolution. We compute $\mathrm{depth}\ L(I)^k$ and show that
$\mathrm{depth}\ L(I)^k=n$ for all $k\geq n$.
