A033177 -id:A033177 - cp's OEIS frontend

A081366 Number of distinct edge lengths in the convex hull of the maximal volume arrangements of n points on a sphere.

1, 2, 1, 2, 3, 3, 3, 8, 1, 11, 3, 5, 3, 14, 8, 25, 9, 29, 16, 11, 18, 34, 37, 6

Offset: 4

Hugo Pfoertner, Mar 19 2003

			a(8)=3 because the corresponding arrangement has 6 edges of length 1.1383499, 8 edges of length 1.264911.. and 4 edges of length 1.4554505, i.e. 3 distinct edge lengths.

See under A081314.

Hugo Pfoertner, Maximal Volume Arrangements: List of edges.

Symmetry groups of maximal volume arrangements: A081314. Distinct distances for minimal energy configurations: A033177.

A133491 Order of the symmetry group of the (in some cases conjectural) minimal-energy configuration of n identical charged particles confined to the surface of a sphere.

Original entry on oeis.org

12, 24, 12, 48, 20, 16, 12, 16, 4, 120, 4

Offset: 3

Keenan Pepper, Nov 30 2007

a(0), a(1) and a(2) are all infinite, because their symmetry groups are continuous (they contain rotations with arbitrary angles). Actual symmetry groups: 3 D_{3h}, 4 T_{d}, 5 D_{3h}, 6 O_{d}, 7 D_{5h}, 8 D_{4d}, 9 D_{3h}, 10 D_{4h}, 11 D_{1h}, 12 I_{d}, 13 D_{1h}.

			a(3)=12 because the minimal-energy configuration of 3 charged particles on a sphere is an equilateral triangle on the equator, which has symmetry group D_3h of order 12.

K. S. Brown, Min-Energy Configurations of Electrons On A Sphere, MathPages.
R. H. Hardin, N. J. A. Sloane and W. D. Smith, Minimal Energy Configurations of Points on a Sphere
Wikipedia, Thomson Problem.

Cf. A033177, A242617.

cp's OEIS Frontend

A081366 Number of distinct edge lengths in the convex hull of the maximal volume arrangements of n points on a sphere.

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