Apollonian球填充与堆叠多胞形
Apollonian Ball Packings and Stacked Polytopes
摘要：
本文研究了维数为$d\ge 3$的Apollonian $d$ -球填充与堆叠$(d+1)$ -多面体之间的关系.对于$d=3$，我们证明了堆叠的$4$ -多面体的$1$ -骨架是阿波罗$3$ -球填充的切线图当且仅当没有六个$4$ -团共享一个$3$ -团.对于高维情形，我们得到了一些部分结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
