  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.
