Geodesic
Six and Seven Dimensional Non-Lattice Sphere Packings
Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 151-155

Voir la notice de l'article provenant de la source Cambridge University Press

The densest lattice packings of equal spheres in Euclidean spaces En of n dimensions are known for n ⩽ 8. However, it is not known for any n ⩾ 3 whether there can be any non-lattice sphere packing with density exceeding that of the densest lattice packing. W. Barlow described [1] a non-lattice packing in E3 with the same density as the densest lattice packing, and I described [6] three non-lattice packings in E5 which also have this property. 
Leech, John. Six and Seven Dimensional Non-Lattice Sphere Packings. Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 151-155. doi: 10.4153/CMB-1969-014-1
@article{10_4153_CMB_1969_014_1,
     author = {Leech, John},
     title = {Six and {Seven} {Dimensional} {Non-Lattice} {Sphere} {Packings}},
     journal = {Canadian mathematical bulletin},
     pages = {151--155},
     year = {1969},
     volume = {12},
     number = {2},
     doi = {10.4153/CMB-1969-014-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-014-1/}
}
TY  - JOUR
AU  - Leech, John
TI  - Six and Seven Dimensional Non-Lattice Sphere Packings
JO  - Canadian mathematical bulletin
PY  - 1969
SP  - 151
EP  - 155
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-014-1/
DO  - 10.4153/CMB-1969-014-1
ID  - 10_4153_CMB_1969_014_1
ER  - 
%0 Journal Article
%A Leech, John
%T Six and Seven Dimensional Non-Lattice Sphere Packings
%J Canadian mathematical bulletin
%D 1969
%P 151-155
%V 12
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-014-1/
%R 10.4153/CMB-1969-014-1
%F 10_4153_CMB_1969_014_1

[1] 1. Barlow, W., Probable nature of the internal symmetry of crystals. Nature 29 (1883) 186–188. Google Scholar

[2] 2. Coxeter, H.S.M., Extreme forms. Canad. J. Math. 3 (1951) 391–441. Google Scholar

[3] 3. Coxeter, H.S.M., Twelve geometric essays. Southern Illinois Univ. Press, 1968). Google Scholar

[4] 4. Leech, J., Some sphere packings in higher space. Canad. J. Math. 16 (1964) 657–682. Google Scholar

[5] 5. Leech, J., Notes on sphere packings. Canad. J. Math. 19 (1967) 251–267. Google Scholar

[6] 6. Leech, J., Five-dimensional non-lattice sphere packings. Canad. Math. Bull. 10 (1967) 387–393. Google Scholar

Cité par Sources :