  Given a simplicial complex we associate to it a squarefree monomial ideal
which we call the face ideal of the simplicial complex, and show that it has
linear quotients. It turns out that its Alexander dual is a whisker complex. We
apply this construction in particular to chain and antichain ideals of a finite
partially ordered set. We also introduce so-called higher dimensional whisker
complexes and show that their independence complexes are shellable.
