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首页> 外文期刊>Contributions to Discrete Mathematics >Hyperball packings related to truncated cube and octahedron tilings in hyperbolic space
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Hyperball packings related to truncated cube and octahedron tilings in hyperbolic space

机译：与截断的立方体和八面体划线相关的间隙包装在双曲线空间中

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In this paper, we study congruent and noncongruent hyperball (hypersphere) packings to the truncated regular cube and octahedron tilings. These are derived from the Coxeter truncated orthoscheme tilings ${4,3,p}$ $(6 p in mathbb{N})$ and ${3,4,p}$ $(4 p in mathbb{N})$, respectively, by their Coxeter reflection groups in hyperbolic space $mathbb{H}^{3}$. We determine the densest hyperball packing arrangement and its density with congruent and noncongruent hyperballs. We prove that the locally densest (noncongruent half) hyperball configuration belongs to the truncated cube with a density of approximately $0.86145$ if we allow $6 p in mathbb{R}$ for the dihedral angle $2pi/p$. This local density is larger than the B"or"oczky--Florian density upper bound for balls and horoballs. But our locally optimal noncongruent hyperball packing configuration cannot be extended to the entire hyperbolic space $mathbb{H}^3$. We determine the extendable densest noncongruent hyperball packing arrangement to the truncated cube tiling ${4,3,p=7}$ with a density of approximately $0.84931$.
机译：在本文中，我们将一致性和非协和的Hyperball（Hypersphere）填充到截短的常规立方体和八面体划线。这些源自Coxeter截短的orthoscheme tilings $ {4,3，p } $（6 in mathbb {n}）$和$ {3,4，p } $ $（4 < p in mathbb {n}）分别由双曲线空间$ mathbb {h} ^ {3} $分别为其Coxeter反射组。我们确定了最浓度的长期包装布置及其密度，与一致性和非团结的连体。我们证明了当地密度最密集的（非协和半）Hyperball配置属于截断的多维数据集，如果我们允许 MathBB {R} $ 2 PI / P $ 6 In mathbb {r} $ 6 。这种局部密度大于B “或”OCZKY - Florian密度上限为球和Horoballs。但我们局部最佳的非协和间隔包装配置不能扩展到整个双曲空间$ MATHBB {H} ^ 3 $。我们将可扩展的密度不全的长度填充布置排列到截断的多维数据集$ {4,3，p = 7 } $，密度约为0.84931 $。

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