Abstract
We consider packings of radius r collars about hyperplanes in \({\mathbb{H}^n}\). For such packings, we prove that the Delaunay cells are truncated ultra-ideal simplices which tile \({\mathbb{H}^n}\). If we place n + 1 hyperplanes in \({\mathbb{H}^n}\) each at a distance of exactly 2r to the others, we could place radius r collars about these hyperplanes. The density of these collars within the corresponding Delaunay cell is an upper bound on density for all packings of radius r collars.
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Przeworski, A. An upper bound on density for packings of collars about hyperplanes in \({\mathbb{H}^n}\) . Geom Dedicata 163, 193–213 (2013). https://doi.org/10.1007/s10711-012-9745-x
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DOI: https://doi.org/10.1007/s10711-012-9745-x