(Slide 14)

The definition of a cell complex requires that the boundary of any cell be composed of a finite set of other cells in the complex. Here we have an illustration of the face relation for a simple cube complex. To the left is an illustration of the face relation for 1-cells. Each 1-cell has two arrows emanating from it, and these arrows point to 0-cells -- the faces of the one cell. On the right the arrows represent the face relation for the 2-cell -- they point to the 1-cells that are the its faces.