%I A000002 %S A000002 24,12,48,20,8,12,16,2,120,4,24,12,24,4,6,2,8,2,20,6,4, %T A000002 2,2,20,12,4,4,1,120,2,4,4,2,20,24,12,24,12,6,2,4,2,12,1,8,1,24 %N A000002 Order of symmetry group of n points on 3-dimensional sphere with maximum distance of any point on the sphere from the closest one of the n points minimized, aka. petrol station placement problem %D A000002 R.H.Hardin, N.J.A.Sloane, W.D.Smith: Spherical Codes, library of putatively optimal coverings of the sphere with n equal caps %D A000002 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 A000002 Hugo Pfoertner (hugo@pfoertner.org) %O A000002 4,1 %K A000002 nonn,more %C A000002 Correctness depends on optimality of configurations, very hard for higher n %C A000002 Order 24 means either tetrahedron symmetry (n=4,16,40,..??) %C A000002 or dihedral symmetry (n=14,38,50,..??) %C A000002 Order 12 means either group A4 (n=28,46,..??) or dihedral symm. (n=5,9,15,39,41,..??) %C A000002 Order 2 means either mirror symmetry (n=25,33,45,..??) or else cyclic symm.