On simplicial and cubical complexes with short links

We consider closed simplicial and cubical $n$-complexes in terms of link of their $(n-2)$-faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every $(n-2)$-face is contained in 3 or 4 $n$-faces. Such simplicial complexes with {\em short} (i.e. of length 3 or 4) links are completely classified by their {\em characteristic partition}. We consider also embedding into hypercubes of the skeletons of simplicial and cubical complexes.