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arXiv · 1306.2515

Apollonian Ball Packings and Stacked Polytopes

Hao Chen
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Abstract

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 no six $4$-cliques share a $3$-clique. For higher dimension, we have some partial results.

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Hao Chen. 2013-12-23. Apollonian Ball Packings and Stacked Polytopes. https://doi.org/10.1007/s00454-016-9777-3

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