Now we could define division of facets.
Facets of n-cube ..., where each component is given by a[xixj...xk] for some i, j, ..., k.
Note that facets of ...
Shown on the left is the division on 3-cube. As you see, a facet of 3-cube is 2-cube and it is divided into two triangles, a[x1x2] and a[x2x1].
Shown on the right is the division on 4-cube. A facet of 4-cube is 3-cube and it is divided into six tetrahedrons a[x1x2x3], ...