The Packing Density of the ...-Dimensional Cross-Polytope

The Packing Density of the ...-Dimensional Cross-Polytope

The packing density of the regular cross-polytope in Euclidean ...-space is unknown except in dimensions ... and ... where it is 1. The only non-trivial upper bound is due to Gravel et al. [Discrete Comput Geom 46(4):799-818, 2011 ], who proved that for ... the packing density of the regular octahed...

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Veröffentlicht in:Discrete & computational geometry 2015-07, Vol.54 (1), p.182-194
Hauptverfasser: Tóth, G Fejes, Fodor, F, Vígh, V
Format: Artikel
Sprache:eng
Schlagworte:
Computational geometry
Euclidean geometry
Geometry
Gravel
Octahedrons
Packing density
Polytopes
Texts
Upper bounds
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Zusammenfassung:The packing density of the regular cross-polytope in Euclidean ...-space is unknown except in dimensions ... and ... where it is 1. The only non-trivial upper bound is due to Gravel et al. [Discrete Comput Geom 46(4):799-818, 2011 ], who proved that for ... the packing density of the regular octahedron is at most ... In this paper, we prove upper bounds for the packing density ... of the ...-dimensional regular cross-polytope ... It turns out that ... approaches zero exponentially fast with growing dimension. Our bound is non-trivial, that is, less than 1, for ...
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-015-9699-5