We determine the optimal horoball packings of the asymptotic or Koszul-type Coxeter simplex tilings of hyperbolic 5-space, where the symmetries of the packings are derived from Coxeter groups. The packing density $$\varTheta = \frac{5}{7 \zeta (3)} \approx 0.5942196502\ldots $$ Θ = 5 7 ζ ( 3 ) ≈ 0.5942196502 … is optimal and realized in eleven cases in a commensurability class of arithmetic Coxeter tilings. For the optimal packing arrangements, horoballs are centered at each ideal vertex of the tiling, and horoballs of different types are used. The packings constructed give an effective proof for a new lower bound for the packing density in $$\overline{{\mathbb {H}}}^5$$ H ¯ 5 .

中文翻译：

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双曲 5 空间中新的 horoball 堆积密度下界

我们确定了双曲 5 空间的渐近或 Koszul 型 Coxeter 单纯形拼贴的最佳 horoball 填充，其中填充的对称性来自 Coxeter 群。堆积密度 $$\varTheta = \frac{5}{7 \zeta (3)} \approx 0.5942196502\ldots $$ Θ = 5 7 ζ ( 3 ) ≈ 0.5942196502 ... 是最优的，并在一个可公度类的 11 种情况下实现算术 Coxeter 平铺。为了优化包装布置，horoballs 以瓷砖的每个理想顶点为中心，并使用不同类型的 horoballs。构造的填充为 $$\overline{{\mathbb {H}}}^5$$ H¯ 5 中的填充密度的新下限提供了有效证明。