Apollonian Ball Packings and Stacked Polytopes
Hao Chen · Discrete & Computational Geometry · 2016
We investigate in this paper the relation between Apollonian d-ball packings and stacked $$(d+1)$$ -polytopes for dimension $$d\ge 3$$ . 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.