How should one place n points on a sphere so as to
minimize the potential energy
This directory contains putatively optimal arrangements for n = 4, ..., 132.
R. H. Hardin, N. J. A. Sloane and W. D. Smith, Spherical Codes, book in preparation.
A library of arrangements of points on a sphere with
(conjecturally) minimal 1/r potential.
How should one place n points on a sphere so as to
minimize the potential energy
This directory contains putatively optimal arrangements for n = 4, ..., 132.
Arrangements of points on a sphere with minimal 1/r potential
Copyright R. H. Hardin, N. J. A. Sloane & W. D. Smith, Feb 1994
dim npts potential 3 4 3.6742346 3 5 6.4746915 3 6 9.9852814 3 7 14.4529774 3 8 19.6752879 3 9 25.7599865 3 10 32.7169495 3 11 40.5964505 3 12 49.1652531 3 13 58.8532306 3 14 69.3063633 3 15 80.6702441 3 16 92.9116553 3 17 106.0504048 3 18 120.0844674 3 19 135.0894676 3 20 150.8815683 3 21 167.6416224 3 22 185.2875361 3 23 203.9301907 3 24 223.3470741 3 25 243.8127603 3 26 265.1333263 3 27 287.3026150 3 28 310.4915424 3 29 334.6344399 3 30 359.6039459 3 31 385.5308381 3 32 412.2612747 3 33 440.2040574 3 34 468.9048533 3 35 498.5698725 3 36 529.1224084 3 37 560.6188877 3 38 593.0385036 3 39 626.3890090 3 40 660.6752788 3 41 695.9167443 3 42 732.0781075 3 43 769.1908465 3 44 807.1742631 3 45 846.1884011 3 46 886.1671136 3 47 927.0592707 3 48 968.7134553 3 49 1011.5571827 3 50 1055.1823147 3 51 1099.8192903 3 52 1145.4189643 3 53 1191.9222904 3 54 1239.3614747 3 55 1287.7727208 3 56 1337.0949453 3 57 1387.3832293 3 58 1438.6182506 3 59 1490.7733353 3 60 1543.8304010 3 61 1597.9418302 3 62 1652.9094099 3 63 1708.8796815 3 64 1765.8025779 3 65 1823.6679603 3 66 1882.4415253 3 67 1942.1227004 3 68 2002.8747017 3 69 2064.5334832 3 70 2127.1009016 3 71 2190.6499064 3 72 2255.0011910 3 73 2320.6338837 3 74 2387.0729818 3 75 2454.3696890 3 76 2522.6748718 3 77 2591.8501524 3 78 2662.0464746 3 79 2733.2483575 3 80 2805.3558760 3 81 2878.5228297 3 82 2952.5696753 3 83 3027.5284889 3 84 3103.4651244 3 85 3180.3614429 3 86 3258.2116057 3 87 3337.0007500 3 88 3416.7201968 3 89 3497.4390186 3 90 3579.0912227 3 91 3661.7136993 3 92 3745.2916362 3 93 3829.8443384 3 94 3915.3092696 3 95 4001.7716756 3 96 4089.1540101 3 97 4177.5335996 3 98 4266.8224642 3 99 4357.1391631 3 100 4448.3506343 3 101 4540.5900517 3 102 4633.7365659 3 103 4727.8366168 3 104 4822.8765227 3 105 4919.0006376 3 106 5015.9845957 3 107 5113.9535477 3 108 5212.8135078 3 109 5312.7350799 3 110 5413.5492942 3 111 5515.2932146 3 112 5618.0448823 3 113 5721.8249780 3 114 5826.5215722 3 115 5932.1812858 3 116 6038.8155936 3 117 6146.3424466 3 118 6254.8770278 3 119 6364.3473175 3 120 6474.7563250 3 121 6586.1219496 3 122 6698.3744993 3 123 6811.8272282 3 124 6926.1699742 3 125 7041.4732640 3 126 7157.6692249 3 127 7274.8195047 3 128 7393.0074431 3 129 7512.1073193 3 130 7632.1673789 3 131 7753.2051669 3 132 7875.0453428 3 192 16963.3383865 3 212 20768.0530860 3 272 34515.1932927 3 282 37147.2944185