OFFSET
4,1
COMMENTS
If more than one best packing exists (this occurs for n = 15, 62, 76, 117, ...; see Buddenhagen, Kottwitz link) for a given n, the one with the largest symmetry group is chosen. A conjectured (except n=24) continuation of the sequence starting with n=15 would be: 3 16 4 2 2 12 1 1 1 24 3 2 4 1 1 6 5 6 3 2 1 4 2 24 1 3 1 10 1 2 1 2 1 24 2 12.
REFERENCES
L. Fejes Toth, Lagerungen in der Ebene auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972.
LINKS
James Buddenhagen and D. A. Kottwitz, Multiplicity and Symmetry Breaking in (Conjectured) Densest Packings of Congruent Circles on a Sphere.
D. A. Kottwitz, The Densest Packing of Equal Circles on a Sphere, Acta Cryst. (1991). A47, 158-165
O. R. Musin and A. S. Tarasov, The strong thirteen spheres problem, Discrete Comput. Geom., 48 (2012), 128-141, arXiv:1002.1439 [math.MG], 2010-2012.
O. R. Musin and A. S. Tarasov, The Tammes problem for N=14, Experimental Mathematics, 24 (2015), 460-468, arXiv:1410.2536 [math.MG].
Hugo Pfoertner, Arrangement of points on a sphere. Visualization of the best known solutions of the Tammes problem.
K. Schuette and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Annalen, 123 (1951), 96-124.
K. Schuette and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Annalen, 123 (1951), 96-124.
N. J. A. Sloane, Library of 3-d packings
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Feb 21 2003
STATUS
approved