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A080865 Order of symmetry groups of n points on 3-dimensional sphere with minimal distance between them maximized, aka. hostile neighbor or Tammes problem. 4
24, 12, 48, 6, 16, 12, 4, 10, 120, 8, 8, 3, 16, 4, 2, 2, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

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

REFERENCES

L. Fejes Toth, Lagerungen in der Ebene auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972.

LINKS

Table of n, a(n) for n=4..20.

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

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

A080866 gives the number of shortest edges which make up the rigid framework of the arrangement.

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

Replaced dead link to Schuette, van der Waerden article by Hugo Pfoertner, Jun 23 2011

STATUS

approved

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Last modified April 28 12:16 EDT 2017. Contains 285575 sequences.