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Simplicial complex
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a simplicial complex is a structured <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> composed of <a href="/facts/Point_(geometry)/6YPAvX2a">points</a>, <a href="/facts/Line_segment/V8E0M4qk">line segments</a>, <a href="/facts/Triangle/cRXUwsMn">triangles</a>, and their <i>n</i>-dimensional counterparts, called <a href="/facts/Simplex/0FCfNRN8">simplices</a>, 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 <a href="/facts/Simplicial_set/6DaqXMLT">simplicial set</a> appearing in modern simplicial <a href="/facts/Homotopy_theory/MJwYyRny">homotopy theory</a>. The purely <a href="/facts/Combinatorics/k14xUoKT">combinatorial</a> counterpart to a simplicial complex is an <a href="/facts/Abstract_simplicial_complex/ytwxClsf">abstract simplicial complex</a>. To distinguish a simplicial complex from an abstract simplicial complex, the former is often called a geometric simplicial complex.<i></i>: 7 </p>