%I A000003 %S A000003 24,12,48,20,16,12,16,4,120,4,24,6,12,20,16,4,12,4,24,6,24, %T A000003 2,2,20,12,6,4,6,120,2,4,2,4,20,24,12,24,12,20,4,48,6,12,2,24,3,24, %N A000003 Orders of symmetry groups of n points on 3-dimensional sphere with Sum 1 / dist(P_i,P_j) minimized, potential energy of equally charged particles minimized %D A000003 R.H.Hardin, N.J.A.Sloane, W.D.Smith: Minimal Energy Arrangements of Points on a Sphere, A library of arrangements of points on a sphere with (conjecturally) minimal 1/r potential %D A000003 Walter Moehres (walter.moehres@t-online.de) , Ada Program to determine symmetries of points in 3-d space, private communication, 1992, available on request %A A000003 Hugo Pfoertner (hugo@pfoertner.org) %O A000003 4,1 %K A000003 nonn,more %Y A000003 A033177 Min-Energy Configurations of Electrons On A Sphere %C A000003 Correctness depends on optimality of configurations, very hard for higher n %C A000003 Order 24 means either tetrahedron symmetry (n=4,22,24,40,48,..??) %C A000003 or dihedral symmetry (n=14,38,50,..??) %C A000003 Order 12 means either group A4 (n=16,28,46,..??) %C A000003 or dihedral symm. (n=5,9,20,39,41,..) %C A000003 Order 2 means either mirror symmetry (n=25,33,47,...) or else cyclic symm.