A153054 Number of points in sporadic known universal optima arising in energy-minimizing point configurations on spheres.

12, 120, 16, 27, 56, 240, 112, 162, 100, 275, 891, 552, 4600, 196560

Offset: 1

Author

Jonathan Vos Post, Dec 17 2008

Keywords

• nonn
• more

Comments

From the second column of Table 1, p. 3, of Ballinger et al. This is an unsorted list of, in a sense, the sporadic solutions, which exclude infinite subsequences corresponding to the n points of the n-gon on the 2-sphere (circle), the n+1 points of the simplex on the n-sphere, the 2n points of the cross polytope on the n-sphere and the (q+1)*(1+q^3) points on isotropic subspaces of the q*(1+q^3)/(q+1)-sphere where q is a prime power.

Examples

			120 is in the sequence because of the 120 points which are vertices of the regular 600-cell in dimension 4.
196560 is in the sequence because of the Leech lattice minimal vectors in 24 dimensions.
		

Links

• B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly and A. Schurmann, Experimental study of energy-minimizing point configurations on spheres, arXiv:math/0611451 [math.MG], 2006-2008.

Crossrefs

Cf. A154255.