Simplicial Complex - Closure, Star, and Link

Closure, Star, and Link

Let K be a simplicial complex and let S be a collection of simplices in K.

The closure of S (denoted Cl S) is the smallest simplicial subcomplex of K that contains each simplex in S. Cl S is obtained by repeatedly adding to S each face of every simplex in S.

The star of S (denoted St S) is the set of all simplices in K that have any faces in S. (Note that the star is generally not a simplicial complex itself).

The link of S (denoted Lk S) equals Cl St S - St Cl S. It is the closed star of S minus the stars of all faces of S.