We investigate in this paper the relation between Apollonian d-ball packings and stacked (d + 1)-polytopes for dimension d ≥ 3. For d = 3, the relation is fully described: we prove that the 1-skeleton of a stacked 4-polytope is the tangency graph of an Apollonian 3-ball packing if and only if there is no six 4-cliques sharing a 3-clique. For higher dimension, we have some partial results.