论文标题
最佳的Horoball包装密度用于双曲线$ 3 $ - 空间
Optimal Horoball Packing Densities for Koszul-type tilings in Hyperbolic $3$-space
论文作者
论文摘要
我们确定了$ \ Mathbb {h}^3 $中的Koszul-Type Coxeter Simplex Tilings的最佳Horoball包装密度。我们给出了一个由Busemann功能和对称组参数化的Horoball包装家庭，该组达到了简单的包装密度上限$ d_3（\ infty）= \ left（2 \ sqrt {3}λ\ \ left（\ frac {π} {π} Lobachevsky功能。
We determine the optimal horoball packing densities for the Koszul-type Coxeter simplex tilings in $\mathbb{H}^3$. We give a family of horoball packings parameterized by the Busemann function and symmetry group that achieve the simplicial packing density upper bound $d_3(\infty) = \left( 2 \sqrt{3} Λ\left( \frac{π}{3} \right) \right)^{-1} \approx 0.853276$ where $Λ$ is the Lobachevsky function.
