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.

24, 12, 48, 6, 16, 12, 4, 10, 120, 8, 8

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

Table of n, a(n) for n=4..14.

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], 2010-2012.

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

Crossrefs

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

Cf. A081314, A084827, A242088, A242617, A217695, A268487.

Cf. A342559 (point numbers where records of packing density occur).

Sequence in context: A228437 A079341 A307267 * A040555 A081314 A119872

Adjacent sequences: A080862 A080863 A080864 * A080866 A080867 A080868

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Feb 21 2003

Status

approved