(but not necessarily finite) and every facet has the same dimension. In other words, is pure if is finite and every face is contained in a facet of dimension .

One-dimensional abstract simplicial complexes are mathematically equivalent to simple undirected graphs: the vertex set of the complex can be viewed as the vertex set of a graph, and the two-element facets of the complex correspond to undirected edges of a graph. In this view, one-element facets of