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 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. 5
 24, 12, 48, 6, 16, 12, 4, 10, 120, 8, 8 (list; graph; refs; listen; history; text; internal format)
 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]. 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 Alexey Tarasov, The strong thirteen spheres problem and files for n=14 CROSSREFS A080866 gives the number of shortest edges which make up the rigid framework of the arrangement. Cf. A081314, A084827, A242088, A242617, A217695, A268487. Sequence in context: A033344 A228437 A079341 * A040555 A081314 A119872 Adjacent sequences:  A080862 A080863 A080864 * A080866 A080867 A080868 KEYWORD nonn,hard,more AUTHOR Hugo Pfoertner, Feb 21 2003 EXTENSIONS Dead link to Schuette, van der Waerden article replaced by Hugo Pfoertner, Jun 23 2011 STATUS approved

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Last modified August 21 19:20 EDT 2018. Contains 313955 sequences. (Running on oeis4.)