A cell complex or simply complex in is a set of convex polyhedra (called cells) in satisfying two conditions: (1) Every face of a cell is a cell (i.e. in ), and (2) If and are cells, then their intersection is a common face of both. A simplicial complex is a cell complex whose cells are all simplices.
The body of a complex is the union of all cells. When a subset of is the body of a simplicial complex , then is said to be a triangulation of . For a finite set of points in , a triangulation of is a simplicial complex with .