SPHERE PACKINGS WITH 3 CONTACTS PER SPHERE AND THE PROBLEM OF THE LEAST DENSE SPHERE PACKING

被引：61
|
作者：
KOCH, E [1 ]
FISCHER, W [1 ]
机构：
[1] UNIV MARBURG,WISSENSCH ZENTRUM MAT WISSENSCH,D-35032 MARBURG,GERMANY
来源：
ZEITSCHRIFT FUR KRISTALLOGRAPHIE | 1995年 / 210卷 / 06期
关键词：
SPHERE PACKING; MINIMAL DENSITY; CONTACT NUMBER 3 IN SPHERE PACKINGS;
D O I：
10.1524/zkri.1995.210.6.407
中图分类号：
O7 [晶体学];
学科分类号：
0702 ; 070205 ; 0703 ; 080501 ;
摘要：
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.
引用
收藏
页码：407 / 414
页数：8
相关论文
共 50 条
  • [41] Minkowski circle packings on the sphere
    Tóth, LF
    DISCRETE & COMPUTATIONAL GEOMETRY, 1999, 22 (02) : 161 - 166
  • [42] Four centuries of sphere packings
    Olimpia, OC
    Rus, MD
    Bulletin of the University of Agricultural Sciences and Veterinary Medicine, Vol 61: HORTICULTURE, 2004, 61 : 367 - 372
  • [43] ACCESSIBILITY OF SPHERE PACKINGS IN RN
    BLIND, G
    BLIND, R
    ARCHIV DER MATHEMATIK, 1978, 30 (04) : 438 - 439
  • [44] The antipode construction for sphere packings
    Conway, JH
    Sloane, NJA
    INVENTIONES MATHEMATICAE, 1996, 123 (02) : 309 - 313
  • [45] Densest ternary sphere packings
    Koshoji, Ryotaro
    Ozaki, Taisuke
    PHYSICAL REVIEW E, 2021, 104 (02)
  • [46] On the density of homogeneous sphere packings
    Koch, E
    Sowa, H
    Fischer, W
    ACTA CRYSTALLOGRAPHICA SECTION A, 2005, 61 : 426 - 434
  • [47] Quaternion orders and sphere packings
    Sheydvasser, Arseniy
    JOURNAL OF NUMBER THEORY, 2019, 204 : 41 - 98
  • [48] A taxonomy of crystallographic sphere packings
    Chait-Roth, Devora
    Cui, Alisa
    Stier, Zachary
    JOURNAL OF NUMBER THEORY, 2020, 207 : 196 - 246
  • [49] Random sphere packing
    Blinovsky V.M.
    Problems of Information Transmission, 2005, 41 (4) : 319 - 330
  • [50] Minkowski Circle Packings on the Sphere
    L. Fejes Tóth
    Discrete & Computational Geometry, 1999, 22 : 161 - 166
12345