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An ellipsoid packing in E 3 of unexpected high density
Author(s) -
Wills J. M.
Publication year - 1991
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300006653
Subject(s) - ellipsoid , sphere packing , mathematics , quotient , spheres , degenerate energy levels , geometry , lattice (music) , combinatorics , euclidean space , physics , quantum mechanics , astronomy , acoustics
A. Bezdek and W. Kuperberg constructed a nonlattice packing of congruent ellipsoids in Euclidean 3‐space E 3 with density 0·7459 …, which exceeds the density σ L 2 = 0·74048… of the densest lattice packing of spheres and hence of ellipsoids in E 3 . G. Kuperberg improved this to 0·7533… We improve this slightly to 0·7549…. In our case the quotient of the largest and the smallest halfaxis of the ellipsoids is <42, so the ellipsoids are not too degenerate. If one combines G. Kuperberg's refinement and ours, one obtains a packing density of 0·7585…
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