Sphere packings with three contacts per sphere and the problem of the least dense sphere packing

1 June 1995

journal article
research article
Published by Walter de Gruyter GmbH in Zeitschrift für Kristallographie - Crystalline Materials

Vol. 210 (6) , 407-414
https://doi.org/10.1524/zkri.1995.210.6.407

Abstract

Two procedures to derive all types of sphere packings with three contacts per sphere are described. 52 such types have been found. They are characterized by their shortest meshs and related to Wells' three-connected nets, if possible. It is proved that there exists no sphere packing with contact number three and a density lower than 5.5%, i.e. the density of the Heesch-Laves packing.

Keywords

This publication has 12 references indexed in Scilit:

The status of the kepler conjecture
The Mathematical Intelligencer, 1994
ON THE SPHERE PACKING PROBLEM AND THE PROOF OF KEPLER'S CONJECTURE
International Journal of Mathematics, 1993
Tetragonal sphere packings
Zeitschrift für Kristallographie - Crystalline Materials, 1993
Tetragonal sphere packings
Zeitschrift für Kristallographie, 1991
The geometrical characteristics of theα-ThSi₂structure type and of its parameter field
Zeitschrift für Kristallographie, 1985
A note on the structure of TiMnSi₂ and the tetrahedrally close-packed 'pentagon–sigma' structure
Acta crystallographica Section B, Structural science, crystal engineering and materials, 1983
Über Kugellagerungen, Wirkungsbereichsteilungen und Koordinationszahlen von Punktkonfigurationen mit trigonaler Symmetrie R[unk]m
Zeitschrift für Kristallographie - Crystalline Materials, 1983
Existenzbedingungen homogener Kugelpackungen zu kubischen Gitterkomplexen mit drei Freiheitsgraden
Zeitschrift für Kristallographie, 1974
Existenzbedingungen homogener Kugelpackungen zu kubischen Gitterkomplexen mit weniger als drei Freiheitsgraden *
Zeitschrift für Kristallographie, 1973
Existenzbedingungen homogener Kugelpackungen in Raumgruppen tetragonaler Symmetrie*
Zeitschrift für Kristallographie, 1971