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Search: id:A080865
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| A080865 |
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Order of symmetry groups of n points on 3-dimensional sphere with minimal distance between them maximized, aka. hostile neighbor or Tammes problem. |
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4
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| 24, 12, 48, 6, 16, 12, 4, 10, 120, 8, 8, 3, 16, 4, 2, 2, 12
(list; graph; listen)
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OFFSET
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4,1
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COMMENT
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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
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REFERENCES
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L. Fejes Toth, Lagerungen in der Ebene auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972.
D. A. Kottwitz, The Densest Packing of Equal Circles on a Sphere. Acta Cryst. (1991). A47, 158-165
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.
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LINKS
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James Buddenhagen and D. A. Kottwitz, Multiplicity and Symmetry Breaking in (Conjectured) Densest Packings of Congruent Circles on a Sphere.
Hugo Pfoertner, Arrangement of points on a sphere. Visualization of the best known solutions of the Tammes problem.
N. J. A. Sloane, Library of 3-d packings
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.
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CROSSREFS
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A080866 gives the number of shortest edges which make up the rigid framework of the arrangement.
Sequence in context: A033968 A033344 A079341 this_sequence A040555 A081314 A119872
Adjacent sequences: A080862 A080863 A080864 this_sequence A080866 A080867 A080868
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KEYWORD
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hard,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 21 2003
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