(Slide 6)

The k-cubes are another class of k-cells. A k-cube may be represented by an ordered set of 2**k vertices, and the set of points contained in the k-cube by the convex combination of these vertices. (As was the case for the k-simplex. )In fact, the cubes and the simplexes share many characteristics, the primary differences being in the number of vertices (for a given k -- k+1 for the k-simplex vs. 2**k for the k-cube), and the means of computing the set of faces. (Or equivalently, the differences in the combinatorial properties of the relationship between vertices and faces.