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