  We consider simple polytopes
$P=vc^{k}(\Delta^{n_{1}}\times\ldots\times\Delta^{n_{r}})$, for
$n_1\ge\ldots\ge n_r\ge 1,r\ge 1,k\ge 0$, that is, $k$-vertex cuts of a product
of simplices, and call them {\emph{generalized truncation polytopes}}. For
these polytopes we describe the cohomology ring of the corresponding
moment-angle manifold $\mathcal Z_P$ and explore some topological consequences
of this calculation. We also examine minimal non-Golodness for their
Stanley--Reisner rings and relate it to the property of $\mathcal Z_P$ being a
connected sum of sphere products.
