(Slide 15)

The coface relation is the complement of the face relation -- we simply reverse all the arrows. Thus we see that the cofaces of a given 0-cell is the set of 1-cells for which the 0-cell is a face, and so on. In the illustration on the right, we see that in this case, each 1-cell has a single coface. A cell with only one coface is on the boundary of the complex.