noun

• A set of points, lines, triangles, tetrahedrons, and higher-dimensional simplices that satisfies certain criteria.

  In a simplicial complex, each simplex which is a vertex, edge, or face, etc., of a simplex included in the complex must also be an element of the complex in its own right. Also, the intersection of two simplices must itself be a simplex, such as a vertex or edge, that is shared by both.