** Next:** What is Voronoi diagram
** Up:** Voronoi Diagram and Delaunay
** Previous:** Voronoi Diagram and Delaunay
** Contents**

##

What is cell complex? What is triangulation?

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
.

Komei Fukuda
2004-08-26