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Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings

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Abstract

In this paper we study congruent and non-congruent hyperball (hypersphere) packings of the truncated regular tetrahedron tilings. These are derived from the Coxeter simplex tilings \(\{p,3,3\}\) \((7\le p \in \mathbb {N})\) and \(\{5,3,3,3,3\}\) in 3- and 5-dimensional hyperbolic space. We determine the densest hyperball packing arrangement and its density with congruent hyperballs in \(\mathbb {H}^5\) and determine the smallest density upper bounds of non-congruent hyperball packings generated by the above tilings in \(\mathbb {H}^n, (n=3,5)\).

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  1. Department of Geometry, Budapest University of Technology and Economics Institute of Mathematics, Budapest, 1521, Hungary

    Jenő Szirmai

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  1. Jenő Szirmai
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Correspondence to Jenő Szirmai.

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Szirmai, J. Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings. Rend. Circ. Mat. Palermo, II. Ser 67, 307–322 (2018). https://doi.org/10.1007/s12215-017-0316-8

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