  In an earlier work, we proposed a generalization for the Apollonian packing
in arbitrary dimensions and showed that the resulting object in four, five, and
six dimensions have properties consistent with the Apollonian circle and sphere
packings in two and three dimensions. In this work, we investigate the
generalization in seven and eight dimensions and show that they too have many
of the properties of those in lower dimensions. In particular, the hyperspheres
are tangent or do not intersect; they fill the hyperspace; the object includes
a maximal cluster of mutually tangent hyperspheres; and there exists a
perspective where all hyperspheres in the object have integer curvatures.
