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.

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

Offset: 3

Author

Keenan Pepper, Nov 30 2007

Keywords

• nonn
• more

Comments

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}.

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A033177, A242617.