Editing Simplicial complex (section)

{{Short description|Mathematical set composed of points, line segments, triangles and higher-dimensional simplices}}

[[File:Simplicial complex example.svg|thumb|200px|A simplicial 3-complex.]]

In [[mathematics]], a '''simplicial complex''' is a structured [[Set (mathematics)|set]] composed of [[Point (geometry)|point]]s, [[line segment]]s, [[triangle]]s, and their ''n''-dimensional counterparts, called [[Simplex|simplices]], such that all the faces and intersections of the elements are also included in the set (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 [[Combinatorics|combinatorial]] counterpart to a simplicial complex is an [[abstract simplicial complex]]. To distinguish a simplicial complex from an abstract simplicial complex, the former is often called a '''geometric simplicial complex'''.<ref name=":0">{{cite Matousek 2007}}, Section 4.3</ref>{{rp|page=7}}