What is "simplicial complex"

n. (context topology English) A collection of simplices of various dimensions, connected to one another according to certain rules.

In mathematics, a simplicial complex is a topological space of a certain kind, constructed by the union of points, line segments, triangles, and their n-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex.