cp's OEIS Frontend

A080865 Order of symmetry groups of n points on 3-dimensional sphere with minimal distance between them maximized, also known as hostile neighbor or Tammes problem.

%I A080865 #43 Nov 11 2023 06:08:09
%S A080865 24,12,48,6,16,12,4,10,120,8,8
%N A080865 Order of symmetry groups of n points on 3-dimensional sphere with minimal distance between them maximized, also known as hostile neighbor or Tammes problem.
%C A080865 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.
%D A080865 L. Fejes Toth, Lagerungen in der Ebene auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972.
%H A080865 James Buddenhagen and D. A. Kottwitz, <a href="http://www.buddenbooks.com/jb/pack/sphere/toggles7.pdf">Multiplicity and Symmetry Breaking in (Conjectured) Densest Packings of Congruent Circles on a Sphere.</a>
%H A080865 D. A. Kottwitz, <a href="http://dx.doi.org/10.1107/S0108767390011370">The Densest Packing of Equal Circles on a Sphere</a>, Acta Cryst. (1991). A47, 158-165
%H A080865 O. R. Musin and A. S. Tarasov, <a href="https://doi.org/10.1007/s00454-011-9392-2">The strong thirteen spheres problem</a>, Discrete Comput. Geom., 48 (2012), 128-141, <a href="https://arxiv.org/abs/1002.1439">arXiv:1002.1439 [math.MG]</a>, 2010-2012.
%H A080865 O. R. Musin and A. S. Tarasov, <a href="https://doi.org/10.1080/10586458.2015.1022842">The Tammes problem for N=14</a>, Experimental Mathematics, 24 (2015), 460-468, <a href="https://arxiv.org/abs/1410.2536">arXiv:1410.2536 [math.MG]</a>.
%H A080865 Hugo Pfoertner, <a href="http://www.enginemonitoring.org/sphere/">Arrangement of points on a sphere.</a> Visualization of the best known solutions of the Tammes problem.
%H A080865 K. Schuette and B. L. van der Waerden, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002282445">Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?</a>, Math. Annalen, 123 (1951), 96-124.
%H A080865 K. Schuette and B. L. van der Waerden, <a href="http://dx.doi.org/10.1007/BF02054944">Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?</a>, Math. Annalen, 123 (1951), 96-124.
%H A080865 N. J. A. Sloane, <a href="http://neilsloane.com/packings/dim3">Library of 3-d packings</a>
%Y A080865 A080866 gives the number of shortest edges which make up the rigid framework of the arrangement.
%Y A080865 Cf. A081314, A084827, A242088, A242617, A217695, A268487.
%Y A080865 Cf. A342559 (point numbers where records of packing density occur).
%K A080865 nonn,hard,more
%O A080865 4,1
%A A080865 _Hugo Pfoertner_, Feb 21 2003