A library of the best ways known to us to arrange n points on a sphere in 3 dimensions so as to maximize the volume of the convex hull.

• How should one place n points on a sphere so as to maximize the volume of their convex hull?

  We give putatively optimal arrangements for n = 4, ..., 130.

• Reference:
  R. H. Hardin, N. J. A. Sloane and W. D. Smith, Spherical Codes, book in preparation.

• Go to library of 3-d arrangements

• If you use any of these arrangements, please acknowledge this source.

• See also Neil Sloane's home page

Arrangements of points on a sphere that maximize volume of convex hull

Copyright R. H. Hardin, N. J. A. Sloane & W. D. Smith, Feb 1994

dim npts   volume

  3    4   0.513200239280
  3    5   0.866025403784
  3    6   1.333333333333
  3    7   1.585094193825
  3    8   1.815716104224
  3    9   2.043750115900
  3   10   2.218711131545
  3   11   2.354634495069
  3   12   2.536150710120
  3   13   2.612834152060
  3   14   2.720977899349
  3   15   2.804379381835
  3   16   2.886455392275
  3   17   2.947522984808
  3   18   3.009613252523
  3   19   3.063216277916
  3   20   3.118538793195
  3   21   3.164441616789
  3   22   3.208239995882
  3   23   3.246942024437
  3   24   3.283995205283
  3   25   3.316263522595
  3   26   3.349359872494
  3   27   3.380416038275
  3   28   3.407379722734
  3   29   3.430953110213
  3   30   3.455125752062
  3   31   3.479801809531
  3   32   3.504874080794
  3   33   3.519303997395
  3   34   3.538169676056
  3   35   3.555094309522
  3   36   3.572449099048
  3   37   3.590011474856
  3   38   3.604998357150
  3   39   3.620272988726
  3   40   3.634130342837
  3   41   3.646959646081
  3   42   3.659352012406
  3   43   3.670906343186
  3   44   3.682575909408
  3   45   3.692596781224
  3   46   3.702525744299
  3   47   3.712685744883
  3   48   3.722885381000
  3   49   3.731437691862
  3   50   3.740940879707
  3   51   3.749284500867
  3   52   3.757164601859
  3   53   3.765209637370
  3   54   3.772894966748
  3   55   3.780272402090
  3   56   3.787220285366
  3   57   3.794247440640
  3   58   3.800829234260
  3   59   3.807286456970
  3   60   3.813835126445
  3   61   3.819438572350
  3   62   3.825219246599
  3   63   3.831117276830
  3   64   3.836635206435
  3   65   3.841686359525
  3   66   3.846805685666
  3   67   3.852292843052
  3   68   3.856927771692
  3   69   3.861573754368
  3   70   3.866188741683
  3   71   3.870719066523
  3   72   3.875747022839
  3   73   3.879282211393
  3   74   3.883165521330
  3   75   3.887309632004
  3   76   3.891226481843
  3   77   3.895410053722
  3   78   3.899220139562
  3   79   3.902548465510
  3   80   3.905816863628
  3   81   3.909170684677
  3   82   3.912532626114
  3   83   3.915830784717
  3   84   3.919054567834
  3   85   3.922246536636
  3   86   3.925355534186
  3   87   3.928338092280
  3   88   3.931363959336
  3   89   3.934183118141
  3   90   3.936990804382
  3   91   3.939692027675
  3   92   3.942475019121
  3   93   3.944937865176
  3   94   3.947576552975
  3   95   3.950038708743
  3   96   3.952480450024
  3   97   3.954845708742
  3   98   3.957286716496
  3   99   3.959500907186
  3  100   3.961753339062
  3  101   3.963998828033
  3  102   3.966095849792
  3  103   3.968239491293
  3  104   3.970332396848
  3  105   3.972342837242
  3  106   3.974376834046
  3  107   3.976382883939
  3  108   3.978376856735
  3  109   3.980246024126
  3  110   3.982163979344
  3  111   3.984096951965
  3  112   3.985897840693
  3  113   3.987620040021
  3  114   3.989331393252
  3  115   3.991037623026
  3  116   3.992730465570
  3  117   3.994353426523
  3  118   3.995989690701
  3  119   3.997650241274
  3  120   3.999201806749
  3  121   4.000855279149
  3  122   4.002559429605
  3  123   4.003820576996
  3  124   4.005226779889
  3  125   4.006752164329
  3  126   4.008106676873
  3  127   4.009640708140
  3  128   4.010947167446
  3  129   4.012321591333
  3  130   4.013655508770
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