2015/03/16 by G. Tóth, Tóth, G. Fejes, Ferenc Fodor +3
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Optimization and Packing Problems
paper · doi:10.48550/arxiv.1503.04571
openalex publication_date 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The packing density of the regular cross-polytope in Euclidean n-space is unknown except in dimensions 2 and 4 where it is 1. The only non-trivial upper bound is due to Gravel, Elser, and Kallus (2011) who proved that for n=3 the packing density of the regular octahedron is at most 1-1.4…× 10-12. In this paper, we prove upper bounds for the packing density of the n-dimensional regular cross-polytope in the case that n≥ 7. We use a modification of Blichfeldt's method due to G. Fejes Tóth and W. Kuperberg (1993).