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We consider closed simplicial and cubicaln-complexes in terms of the links 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 4n-faces. Such simplical complexes withshort (i.e., of length 3 or 4) links are completely classified by theircharacteristic partition. We consider also embedding into (the skeletons of) hypercubes of the skeletons of simplical and cubical complexes.

On simplicial and cubical complexes with short links