Simplicial complex

In mathematics, a simplicial complex is a set composed 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.

A simplicial complex ${\displaystyle {\mathcal {K}}}$ is a set of simplices that satisfies the following conditions:

Note that the empty set is a face of every simplex. See also the definition of an abstract simplicial complex, which loosely speaking is a simplicial complex without an associated geometry.

A simplicial k-complex ${\displaystyle {\mathcal {K}}}$ is a simplicial complex where the largest dimension of any simplex in ${\displaystyle {\mathcal {K}}}$ equals k. For instance, a simplicial 2-complex must contain at least one triangle, and must not contain any tetrahedra or higher-dimensional simplices.

...
Wikipedia