Minimal Energy Arrangements of Points on a Sphere

R. H. Hardin, N. J. A. Sloane and W. D. Smith

 A library of arrangements of points on a sphere with (conjecturally) minimal 1/r potential.

Summary of results:

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


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