Search: id:A080865
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%I A080865
%S A080865 24,12,48,6,16,12,4,10,120,8,8,3,16,4,2,2,12
%N A080865 Order of symmetry groups of n points on 3-dimensional sphere with minimal 
               distance between them maximized, aka. hostile neighbor or Tammes 
               problem.
%C A080865 Terms for n > 12 are only conjectures. 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 continuation of the sequence starting with n=21 would 
               be: 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.
%D A080865 D. A. Kottwitz, The Densest Packing of Equal Circles on a Sphere. Acta 
               Cryst. (1991). A47, 158-165
%D A080865 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.
%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 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 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/packings/
               dim3">Library of 3-d packings</a>
%H A080865 K. Schuette and B. L. van der Waerden, <a href="http://www.digizeitschriften.de/
               no_cache/home/jkdigitools/loader/?tx_jkDigiTools_pi1%5BIDDOC%5D=364233">
               Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand 
               Eins Platz?</a>, Math. Annalen, 123 (1951), 96-124.
%Y A080865 A080866 gives the number of shortest edges which make up the rigid framework 
               of the arrangement.
%Y A080865 Sequence in context: A033968 A033344 A079341 this_sequence A040555 A081314 
               A119872
%Y A080865 Adjacent sequences: A080862 A080863 A080864 this_sequence A080866 A080867 
               A080868
%K A080865 hard,nonn
%O A080865 4,1
%A A080865 Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 21 2003

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