Simplicial complex

Summary

An abstract simplicial complex is a family of finite sets closed under taking subsets. Each set of size $k + 1$ stands for a $k$-dimensional simplex: a point, a segment, a triangle, a tetrahedron, and so on. Simplicial complexes describe spaces by finite combinatorial data, and they link combinatorics with topology and commutative algebra through f-vectors and h-vectors, homology and Stanley–Reisner rings.