List of edges of the convex hull of the best known solutions for the problem "maximize minimum mutual distance of N points on the surface of a 3d sphere". Tables of arrangements taken from http://www.research.att.com/~njas/packings/ Changes of these tables after 1997 are not taken into account. In a post-processing step the locations of slack points were moved to maximize their minimal distance from their neigbours. With the exception of N=35 and N=43 all results were already published by D.A. Kottwitz: The Densest Packing of Equal Circles on a Sphere. Acta Cryst. (1991). A47, pp.158-165 Compiled by Hugo Pfoertner, 1997,2001 (contact info: http://www.pfoertner.org) For some of the results (e.g. N=17,43,47) the limited accuracy of the classification before sorting does allow a unique identification of minimal edges. List of edges for N = 4, No of edges: 6 Length Count 1.63299 6 List of edges for N = 5, No of edges: 9 Length Count 1.41421 6 1.73205 3 List of edges for N = 6, No of edges: 12 Length Count 1.41421 12 List of edges for N = 7, No of edges: 15 Length Count 1.25687 12 1.69338 3 List of edges for N = 8, No of edges: 18 Length Count 1.21556 16 1.71907 2 List of edges for N = 9, No of edges: 21 Length Count 1.15470 18 1.49071 3 List of edges for N = 10, No of edges: 24 Length Count 1.09143 19 1.21989 1 1.38443 2 1.54351 2 List of edges for N = 11, No of edges: 27 Length Count 1.05146 25 1.70130 2 List of edges for N = 12, No of edges: 30 Length Count 1.05146 30 List of edges for N = 13, No of edges: 33 Length Count 0.95641 24 1.18789 4 1.28970 4 1.35257 1 List of edges for N = 14, No of edges: 36 Length Count 0.93386 28 1.16787 4 1.27548 4 List of edges for N = 15, No of edges: 39 Length Count 0.90266 30 1.07266 3 1.11280 3 1.25831 3 List of edges for N = 16, No of edges: 42 Length Count 0.88057 32 1.07637 8 1.24532 2 List of edges for N = 17, No of edges: 45 Length Count 0.86244 31 0.86245 3 0.93398 4 0.97797 2 1.10782 1 1.15516 2 1.21060 2 List of edges for N = 18, No of edges: 48 Length Count 0.83822 34 0.85270 2 0.87280 2 0.88676 2 1.06335 2 1.07095 2 1.08160 2 1.08906 2 List of edges for N = 19, No of edges: 51 Length Count 0.80856 34 0.81909 4 0.86100 2 0.87689 2 0.95649 2 0.99512 1 1.03160 1 1.04578 1 1.14903 2 1.23979 1 1.28694 1 List of edges for N = 20, No of edges: 54 Length Count 0.80439 39 0.80766 6 0.95519 6 1.08762 3 List of edges for N = 21, No of edges: 57 Length Count 0.77524 40 0.79234 1 0.79818 1 0.81739 1 0.84573 1 0.85760 1 0.87776 1 0.87901 1 0.88903 1 0.93935 1 0.94058 1 0.96327 1 0.98977 1 0.99511 1 1.01374 1 1.03091 1 1.05865 1 1.06018 1 List of edges for N = 22, No of edges: 60 Length Count 0.76118 42 0.79092 4 0.80640 2 0.83800 4 0.93484 2 0.97484 2 1.02726 4 List of edges for N = 23, No of edges: 63 Length Count 0.74452 43 0.74454 3 0.74521 2 0.74558 1 0.74610 1 0.74969 1 0.75286 1 0.75331 1 0.79290 1 1.04568 1 1.04786 1 1.05095 1 1.05215 2 1.05268 1 1.05313 1 1.05729 1 1.07361 1 List of edges for N = 24, No of edges: 66 Length Count 0.74421 60 1.05247 6 List of edges for N = 25, No of edges: 69 Length Count 0.71078 48 0.73271 3 0.73476 3 0.82071 3 0.91156 3 0.94910 3 0.95744 3 1.00126 2 1.00127 1 List of edges for N = 26, No of edges: 72 Length Count 0.70103 46 0.70128 6 0.73128 2 0.74340 2 0.74957 1 0.78273 2 0.80630 1 0.82903 1 0.84221 2 0.85272 2 0.86325 2 0.89054 2 0.91324 1 1.11662 2 List of edges for N = 27, No of edges: 75 Length Count 0.69514 52 0.69688 2 0.69795 1 0.76540 2 0.76598 4 0.76691 4 0.83326 2 0.83412 4 0.83551 4 List of edges for N = 28, No of edges: 78 Length Count 0.67345 52 0.67388 3 0.67672 1 0.67890 1 0.69755 1 0.70128 1 0.71052 1 0.71781 1 0.73825 1 0.79172 1 0.79985 1 0.80606 1 0.81866 1 0.82090 1 0.83944 1 0.84658 1 0.87422 1 0.88476 1 0.89627 1 0.90371 1 0.90897 1 0.91906 1 0.93073 1 0.94516 1 1.02855 1 List of edges for N = 29, No of edges: 81 Length Count 0.66290 54 0.66522 1 0.66614 1 0.66628 3 0.66708 1 0.66763 1 0.67273 1 0.68337 1 0.69148 1 0.76990 1 0.77704 1 0.78477 1 0.78972 1 0.79121 1 0.80003 1 0.80240 1 0.82641 1 0.88070 1 0.88206 1 0.88927 1 0.89084 1 0.90152 1 0.91426 1 0.96045 1 0.98399 1 0.98856 1 List of edges for N = 30, No of edges: 84 Length Count 0.66098 63 0.67029 6 0.77868 6 0.78849 3 0.88860 6 List of edges for N = 31, No of edges: 87 Length Count 0.64635 60 0.66278 5 0.71905 5 0.72533 5 0.76791 5 0.77610 5 1.04581 2 List of edges for N = 32, No of edges: 90 Length Count 0.64247 66 0.64357 3 0.71483 6 0.71585 6 0.78352 6 0.78446 3 List of edges for N = 33, No of edges: 93 Length Count 0.62226 66 0.62563 3 0.70537 3 0.70784 3 0.71631 3 0.71714 3 0.81205 3 0.81503 3 0.87850 3 0.87909 3 List of edges for N = 34, No of edges: 96 Length Count 0.61484 68 0.63238 2 0.63704 1 0.63705 1 0.64381 2 0.67033 1 0.67246 2 0.72419 2 0.73263 2 0.75678 2 0.75732 2 0.77498 2 0.78702 2 0.82124 1 0.83292 1 0.83293 1 0.87202 1 0.87203 1 0.88231 2 List of edges for N = 35, No of edges: 99 Length Count 0.60673 66 0.60735 1 0.60740 1 0.60780 1 0.61038 1 0.61082 1 0.61270 1 0.61330 1 0.63774 3 0.64052 1 0.65072 1 0.65450 1 0.65932 1 0.67001 1 0.68759 1 0.70337 1 0.71032 1 0.74730 1 0.75045 1 0.77507 1 0.77831 1 0.77938 1 0.78135 1 0.78256 1 0.78423 1 0.78687 1 0.80118 1 0.82190 1 0.82204 1 0.82512 1 0.87703 1 0.88987 1 List of edges for N = 36, No of edges: 102 Length Count 0.60457 72 0.60550 1 0.60551 3 0.60599 2 0.61492 4 0.62262 4 0.76793 4 0.78136 4 0.78569 4 0.79057 4 List of edges for N = 37, No of edges: 105 Length Count 0.59179 66 0.59299 4 0.59381 1 0.59487 2 0.59927 3 0.60572 3 0.60611 2 0.60724 2 0.61322 2 0.66681 1 0.68020 1 0.68318 2 0.69822 1 0.69951 1 0.74949 2 0.76519 2 0.78234 2 0.82007 2 0.82929 2 0.83047 2 0.87930 2 List of edges for N = 38, No of edges: 108 Length Count 0.58893 72 0.61770 12 0.61938 12 0.77438 12 List of edges for N = 39, No of edges: 111 Length Count 0.57621 76 0.57651 1 0.57684 1 0.58228 1 0.58409 1 0.58768 1 0.59296 1 0.59345 1 0.60588 1 0.60881 1 0.62182 1 0.63157 1 0.64087 1 0.64531 1 0.65517 1 0.65923 1 0.65999 1 0.66163 1 0.66295 1 0.68314 1 0.69769 1 0.70836 1 0.70893 1 0.71887 1 0.73287 1 0.73906 1 0.74805 1 0.76003 1 0.76356 1 0.76707 1 0.76733 1 0.78008 1 0.79846 1 0.80315 1 0.80741 1 0.83365 1 List of edges for N = 40, No of edges: 114 Length Count 0.57068 78 0.57627 3 0.58076 3 0.58186 6 0.60806 3 0.61349 3 0.69449 3 0.71889 3 0.72342 3 0.77205 3 0.78109 3 0.81018 3 List of edges for N = 41, No of edges: 117 Length Count 0.56350 81 0.56924 2 0.58166 2 0.58379 2 0.59352 2 0.59459 1 0.59511 2 0.60795 1 0.61231 2 0.63804 1 0.63873 2 0.65576 2 0.65635 2 0.70214 2 0.70505 2 0.72886 2 0.78849 2 0.78965 2 0.79106 2 0.79215 2 0.79564 1 List of edges for N = 42, No of edges: 120 Length Count 0.55977 85 0.56327 10 0.63174 10 0.70830 5 0.75754 10 List of edges for N = 43, No of edges: 123 Length Count 0.55279 54 0.55280 28 0.55339 1 0.55473 1 0.55494 3 0.55598 1 0.55915 1 0.56204 1 0.56219 1 0.56503 1 0.56705 1 0.57043 1 0.57196 1 0.57492 1 0.58117 1 0.58368 1 0.58765 1 0.58766 1 0.59179 1 0.59366 1 0.62678 1 0.62879 1 0.62936 1 0.63786 1 0.65612 1 0.65637 1 0.65960 1 0.66060 1 0.66687 1 0.67081 1 0.68119 1 0.68286 1 0.70067 1 0.70756 1 0.71237 1 0.71431 1 0.75432 1 0.77454 1 0.77693 1 0.78580 1 0.84815 1 List of edges for N = 44, No of edges: 126 Length Count 0.55100 88 0.55146 2 0.55158 2 0.55202 2 0.55252 2 0.55280 2 0.55282 2 0.59266 2 0.59323 2 0.59399 2 0.60030 2 0.63975 2 0.64011 2 0.64228 2 0.64385 2 0.67892 2 0.67905 2 0.68083 1 0.72038 2 0.72529 1 0.76309 2 List of edges for N = 45, No of edges: 129 Length Count 0.53991 84 0.54013 1 0.54077 3 0.54084 3 0.54168 1 0.54487 1 0.54893 1 0.55108 1 0.55724 1 0.56034 1 0.56217 1 0.56250 1 0.56811 1 0.57088 1 0.58796 1 0.58904 1 0.58931 1 0.59039 1 0.59670 1 0.60219 1 0.61184 1 0.61539 1 0.61639 1 0.63473 1 0.64282 1 0.65031 1 0.66131 1 0.66134 1 0.66798 1 0.67242 1 0.68504 1 0.68600 1 0.68891 1 0.69907 1 0.72171 1 0.72356 1 0.72443 1 0.73046 1 0.73596 1 0.75404 1 0.75460 1 0.75584 1 List of edges for N = 46, No of edges: 132 Length Count 0.53379 91 0.53421 1 0.53422 1 0.53449 2 0.53675 2 0.53723 2 0.54710 2 0.54822 2 0.55418 2 0.55512 2 0.55992 2 0.58454 2 0.60025 2 0.61426 2 0.64177 2 0.65157 2 0.68717 2 0.71641 2 0.75232 1 0.75434 2 0.75442 2 0.85156 2 0.85918 2 List of edges for N = 47, No of edges: 135 Length Count 0.53081 87 0.53082 5 0.53095 1 0.53098 4 0.53112 1 0.53125 1 0.53170 1 0.53171 1 0.53196 1 0.53202 1 0.53211 1 0.53213 1 0.53235 1 0.53440 1 0.53565 1 0.53620 1 0.53712 1 0.53852 1 0.53970 1 0.63723 1 0.64450 1 0.64484 1 0.64522 1 0.64564 1 0.64566 1 0.64581 1 0.64596 1 0.64598 1 0.64616 1 0.64641 1 0.64719 1 0.64790 1 0.64912 1 0.65549 1 0.65571 1 0.74660 1 0.74773 1 0.74837 1 0.74947 1 0.75026 1 0.75043 1 0.75047 1 List of edges for N = 48, No of edges: 138 Length Count 0.53049 120 0.64544 12 0.75022 6 List of edges for N = 49, No of edges: 141 Length Count 0.51635 96 0.51746 2 0.51786 2 0.51893 2 0.52633 2 0.53320 2 0.53837 2 0.54301 2 0.54380 2 0.57250 1 0.57251 1 0.57332 2 0.58848 2 0.59454 2 0.59546 1 0.59547 1 0.62138 2 0.67365 2 0.67996 2 0.68950 2 0.69103 2 0.69338 2 0.69858 2 0.69884 1 0.71972 2 0.73995 2 List of edges for N = 50, No of edges: 144 Length Count 0.51347 102 0.53272 12 0.61024 12 0.62313 6 0.63633 12