The best known packings of equal 5d hyperspheres in a larger 5d container hypersphere (complete up to N = 300)

Last update: 01-Aug-2025


Download    Results    History of updates    References

Radii plots

2-50   50-100   100-150   150-200   200-250   250-300  

Density plots

2-50   50-100   100-150   150-200   200-250   250-300  

Contacts plots

2-50   50-100   100-150   150-200   200-250   250-300  

Rattlers plots

2-50   50-100   100-150   150-200   200-250   250-300  

Boundary plots

2-50   50-100   100-150   150-200   200-250   250-300  

Core plots

2-50   50-100   100-150   150-200   200-250   250-300  


Download

You may download ASCII files which contain all the values of radius, ratio etc. by using the links given in the table header below.
All coordinates of all packings are packed as ASCII files here.


Results

The table below summarizes the current status of the search.

Legend:
N
the number of hyperspheres (called objects here); colors correspond to active researchers in the past, see "References" at the bottom of the page
radius
of the objects in the container hypersphere (which has always unit radius)
distance
packing of objects in a hypersphere is equivalent to distributing points in a hypersphere; the latter are then the centers of the objects. "distance" is here the largest distance between these points
ratio
= 1/radius
density
ratio of total volume occupied by the objects to container volume
contacts
number of mutual contacts between objects plus number of contacts between objects and container
loose
number of objects that have still degrees of freedom for a movement inside the container (so called "rattlers")
boundary
number of objects that have contact to the container (possible contacts of rattlers with the container are suppressed)
core
number of objects that don't have contact to the container (possible contacts of rattlers with the container are suppressed)
reference
for the best known packing so far
records
the sequence of N 's that establish density records

N radius distance ratio density contacts loose boundary core reference
1 1.000000000000 1.0000000000 1.000000000000
2 0.500000000000 2.000000000000 2.0000000000 0.062500000000 3 2
3 0.464101615138 1.732050807571 2.1547005384 0.064593178207 6 3
4 0.449489742783 1.632993161854 2.2247448714 0.073393723246 10 4
5 0.441518440112 1.581138830083 2.2649110641 0.083890781045 15 5
6 0.436491673104 1.549193338485 2.2909944487 0.095067279504 21 6 [2]
7 0.414213562373 1.414213562373 2.4142135624 0.085353161737 18 1 7 [2]
8 0.414213562373 1.414213562373 2.4142135624 0.097546470558 32 8 [2]
9 0.414213562373 1.414213562373 2.4142135624 0.109739779378 32 1 9 [2]
10 0.414213562373 1.414213562373 2.4142135624 0.121933088198 50 10 [2]
11 0.397031990187 1.316925554011 2.5186887322 0.108522599667 46 11 [2]
12 0.394090243925 1.300821582666 2.5374898654 0.114066906652 52 12 [2]
13 0.389302395185 1.274943252161 2.5686972707 0.116246190872 59 13 [2]
14 0.387425886723 1.264911064068 2.5811388301 0.122200002334 75 14 [2]
15 0.387425886723 1.264911064068 2.5811388301 0.130928573930 85 15 [2]
16 0.387425886723 1.264911064068 2.5811388301 0.139657145525 96 16 [2]
17 0.376541254138 1.207910729097 2.6557514987 0.128680205329 81 17 [2]
18 0.375730144461 1.203742711993 2.6614846180 0.134788457244 93 18 [2]
19 0.373061825115 1.190107222880 2.6805208485 0.137295927042 99 19 [2]
20 0.371807018165 1.183735027026 2.6895673055 0.142107798517 111 1 20 [2]
21 0.369192816110 1.170540937195 2.7086117507 0.144040792980 108 21 [2]
22 0.362201383116 1.135786041323 2.7608950341 0.137142860229 103 22 [2]
23 0.359528550591 1.122699695428 2.7814202748 0.138163954707 103 2 23 [2]
24 0.358711229094 1.118719819738 2.7877577251 0.142539785827 130 24 [2]
25 0.357717203586 1.113893149819 2.7955043536 0.146433062026 136 25 [2]
26 0.355736147889 1.104318197345 2.8110722116 0.148119875323 134 26 [2]
27 0.353572832675 1.093929372239 2.8282715966 0.149196351808 155 27 [31]
28 0.352323542112 1.087961551855 2.8383002566 0.152007966409 140 28 [2]
29 0.351770147780 1.085325356663 2.8427653862 0.156204270861 167 29 [2]
30 0.351383324479 1.083485324199 2.8458948685 0.160704112926 186 30 [2]
31 0.347266521499 1.064037721174 2.8796326110 0.156558365293 183 31 [2]
32 0.345671614990 1.056569217870 2.8929190499 0.157931431452 166 32 [31]
33 0.341937742977 1.039226119802 2.9245089802 0.154258514035 149 4 33 [2]
34 0.339736538271 1.029093863172 2.9434573187 0.153882843692 156 4 34 [2]
35 0.338040853747 1.021334490687 2.9582223241 0.154494845269 171 1 35 [2]
36 0.336842539810 1.015874992083 2.9687461701 0.156112316185 178 2 36 [2]
37 0.334697769391 1.006152554410 2.9877701361 0.155405295694 186 37 [2]
38 0.334165454510 1.003749225009 2.9925295584 0.158340259610 218 38 [2]
39 0.333338045552 1.000021205133 2.9999575906 0.160505171711 171 1 39 [31]
40 0.333333333333 1.000000000000 3.0000000000 0.164609053498 280 40 [2]
41 0.333333333333 1.000000000000 3.0000000000 0.168724279835 320 40 1 [31]
42 0.329830585092 0.984320017461 3.0318595218 0.163947166918 196 1 41 1 [31]
43 0.329216819339 0.981589368459 3.0375118805 0.166294746470 211 3 42 1 [31]
44 0.327725969866 0.974977331195 3.0513297448 0.166343932140 212 1 43 1 [31]
45 0.327087178530 0.972153206460 3.0572888992 0.168472925225 234 1 44 1 [31]
46 0.325303022845 0.964293701794 3.0740568939 0.167570793572 186 7 45 1 [31]
47 0.324536901691 0.960931552008 3.0813136959 0.169206984734 214 2 46 1 [31]
48 0.323974620314 0.958468809158 3.0866615386 0.171315313440 226 1 47 1 [31]
49 0.322910642558 0.953819873282 3.0968319659 0.172031459608 247 1 48 1 [31]
50 0.322476309552 0.951926298957 3.1010029896 0.174364905870 354 4 50 [31]
51 0.322476309552 0.951926298957 3.1010029896 0.177852203987 358 4 50 1 [31]
52 0.320576761950 0.943673233403 3.1193776926 0.176061149561 202 13 51 1 [31]
53 0.319248966799 0.937931640876 3.1323515626 0.175761346748 268 1 52 1 [31]
54 0.317572653505 0.930714910931 3.1488857399 0.174425207787 234 8 53 1 [31]
55 0.316519872045 0.926200657778 3.1593592956 0.174730048291 266 4 54 1 [31]
56 0.315626705991 0.922381714056 3.1682997066 0.175410966447 266 5 55 1 [31]
57 0.314963442306 0.919552215917 3.1749716497 0.176675202280 285 3 56 1 [31]
58 0.314928120694 0.919401686763 3.1753277472 0.179673985527 368 2 57 1 [31]
59 0.313862254708 0.914866604735 3.1861110567 0.179699745926 282 7 58 1 [31]
60 0.312436045512 0.908820316925 3.2006550280 0.178631033946 272 4 59 1 [31]
61 0.310778659708 0.901825412360 3.2177241544 0.176842148209 292 2 60 1 [31]
62 0.310010194385 0.898593549824 3.2257003741 0.177529923778 287 6 61 1 [31]
63 0.309268262711 0.895480100349 3.2334387992 0.178244986442 301 1 62 1 [31]
64 0.308042827978 0.890352294717 3.2463018424 0.177515174135 285 8 63 1 [31]
65 0.307425672093 0.887776689679 3.2528187812 0.178490050516 301 3 64 1 [31]
66 0.306738049784 0.884912404866 3.2601107059 0.179218234918 328 4 65 1 [31]
67 0.306564517411 0.884190454940 3.2619561078 0.181419613704 392 6 66 1 [31]
68 0.305801821336 0.881021675754 3.2700917072 0.181848302448 333 4 67 1 [31]
69 0.304885263752 0.877222846397 3.2799223803 0.181773788873 344 7 68 1 [31]
70 0.304455567220 0.875445342875 3.2845515329 0.183112351363 342 7 69 1 [31]
71 0.304379689368 0.875131690998 3.2853703283 0.185496917089 317 15 70 1 [31]
72 0.304130517676 0.874102185543 3.2880620059 0.187340856887 428 3 71 1 [31]
73 0.304130517676 0.874102185543 3.2880620059 0.189942813233 438 3 72 1 [31]
74 0.304113535976 0.874032048899 3.2882456113 0.192491020081 537 3 73 1 [31]
75 0.304113535976 0.874032048899 3.2882456113 0.195092250082 552 3 74 1 [31]
76 0.302265228198 0.866418703535 3.3083527535 0.191758463876 413 3 75 1 [31]
77 0.300355546422 0.858594804507 3.3293874940 0.188221402764 355 6 76 1 [31]
78 0.298892813532 0.852630865297 3.3456809757 0.186068119493 376 1 77 1 [31]
79 0.297814029797 0.848248305818 3.3578001704 0.185077173032 374 2 78 1 [31]
80 0.296801219787 0.844146002919 3.3692583902 0.184254623455 387 7 79 1 [31]
81 0.295844413483 0.840281378570 3.3801550897 0.183570073912 388 1 80 1 [31]
82 0.295273306088 0.837979627106 3.3866928685 0.184049561094 390 2 81 1 [31]
83 0.294510754235 0.834912101079 3.3954617467 0.183900911599 391 3 82 1 [31]
84 0.293226334874 0.829760217004 3.4103348883 0.182093375342 406 1 83 1 [31]
85 0.292664068381 0.827510819961 3.4168868270 0.182501296179 411 1 84 1 [31]
86 0.292168344145 0.825530595385 3.4226842847 0.183089840901 411 2 85 1 [31]
87 0.291611421154 0.823309211532 3.4292209682 0.183460215648 398 5 86 1 [31]
88 0.291141870558 0.821439039677 3.4347515803 0.184079748384 416 3 87 1 [31]
89 0.290572012968 0.819172680750 3.4414876704 0.184356696243 426 2 88 1 [31]
90 0.289994175103 0.816878298555 3.4483451250 0.184581802471 429 2 89 1 [31]
91 0.289462619987 0.814770983567 3.4546774988 0.184928495193 439 1 90 1 [31]
92 0.288731627217 0.811878155322 3.4634238363 0.184611869179 445 1 91 1 [31]
93 0.288349405490 0.810367918511 3.4680147798 0.185386561873 450 1 92 1 [31]
94 0.287750524909 0.808004877427 3.4752325832 0.185442159585 446 3 93 1 [31]
95 0.287331624237 0.806354355009 3.4802991236 0.186054742495 461 1 94 1 [31]
96 0.286968139271 0.804923749067 3.4847074053 0.186827000673 466 1 95 1 [31]
97 0.286421709326 0.802775849740 3.4913554645 0.186982686544 466 2 96 1 [31]
98 0.285943287639 0.800897975438 3.4971969731 0.187337882302 471 2 97 1 [31]
99 0.285637532687 0.799699160460 3.5009404772 0.188239846357 481 1 98 1 [31]
100 0.284995743161 0.797186143817 3.5088243386 0.188014725982 486 1 99 1 [31]
101 0.284704110761 0.796045706523 3.5124185504 0.188925274983 492 1 100 1 [31]
102 0.284049933676 0.793490906801 3.5205077750 0.188613872927 496 1 101 1 [31]
103 0.283265979150 0.790435422094 3.5302509783 0.187849184701 501 1 102 1 [31]
104 0.282838818861 0.788773364481 3.5355825768 0.188247151833 472 7 103 1 [31]
105 0.282566897927 0.787716365778 3.5389849531 0.189145371561 511 1 104 1 [31]
106 0.282139366481 0.786056104227 3.5443476480 0.189506582367 510 2 105 1 [31]
107 0.281572335014 0.783857161234 3.5514852691 0.189379815653 511 3 106 1 [31]
108 0.281179770305 0.782336831072 3.5564436194 0.189820937763 520 2 107 1 [31]
109 0.280778985785 0.780786379251 3.5615200945 0.190217076581 525 2 108 1 [31]
110 0.280306546019 0.778960943631 3.5675228217 0.190352631533 526 2 109 1 [31]
111 0.279694611460 0.776600080771 3.5753280865 0.189995570428 537 1 110 1 [31]
112 0.279276464961 0.774989164037 3.5806812441 0.190278498497 541 2 111 1 [31]
113 0.279025914150 0.774024807899 3.5838965103 0.191117801863 538 2 112 1 [31]
114 0.278590732700 0.772351410851 3.5894948490 0.191310223515 556 1 113 1 [31]
115 0.278159041596 0.770693428677 3.5950655936 0.191497781431 560 1 114 1 [31]
116 0.277761932549 0.769170014894 3.6002053659 0.191788081548 560 2 115 1 [31]
117 0.277317071723 0.767465401138 3.6059806697 0.191897311493 555 4 116 1 [31]
118 0.276853263301 0.765690417314 3.6120217189 0.191924422322 571 2 117 1 [31]
119 0.276448079496 0.764141650826 3.6173157789 0.192138699773 581 1 118 1 [31]
120 0.276051011179 0.762625586724 3.6225188806 0.192365841910 583 118 2 [31]
121 0.275606325778 0.760929686676 3.6283637437 0.192411611609 586 2 119 2 [31]
122 0.275215725112 0.759441766737 3.6335133089 0.192630944621 596 1 120 2 [31]
123 0.274741756302 0.757638423801 3.6397816388 0.192543322781 606 121 2 [31]
124 0.274379169429 0.756260454136 3.6445915413 0.192831229681 604 1 122 2 [31]
125 0.274037040747 0.754961495636 3.6491417265 0.193177418538 611 1 124 1 [31]
126 0.273680332016 0.753608484197 3.6538979350 0.193458798112 611 2 124 2 [31]
127 0.273309817996 0.752204515113 3.6588513627 0.193677818929 602 3 125 2 [31]
128 0.272917787078 0.750720571148 3.6641070951 0.193806873534 621 2 126 2 [31]
129 0.272559163988 0.749364485728 3.6689281893 0.194041066352 625 2 127 2 [31]
130 0.272090961984 0.747596053281 3.6752415174 0.193871483192 640 128 2 [31]
131 0.271707170667 0.746148141856 3.6804328629 0.193988862372 645 129 2 [31]
132 0.271403075476 0.745001979396 3.6845566258 0.194378288829 650 130 2 [31]
133 0.271089365865 0.743820581481 3.6888204626 0.194721564065 655 131 2 [31]
134 0.270580994338 0.741908264626 3.6957510724 0.194352996272 651 2 132 2 [31]
135 0.270305180100 0.740871862396 3.6995221462 0.194807472302 657 133 2 [31]
136 0.269932741250 0.739473625244 3.7046265502 0.194902196677 656 3 134 2 [31]
137 0.269791288446 0.738942946522 3.7065689028 0.195821412176 674 135 2 [31]
138 0.269480616542 0.737778141536 3.7108420369 0.196117680380 681 136 2 [31]
139 0.269139984004 0.736502142992 3.7155386023 0.196293496753 680 1 137 2 [31]
140 0.268740725418 0.735008046419 3.7210586466 0.196243581531 671 4 138 2 [31]
141 0.268366587573 0.733609436133 3.7262462851 0.196273348735 677 2 139 2 [31]
142 0.268069879552 0.732501292303 3.7303706096 0.196575070649 684 3 140 2 [31]
143 0.267806462425 0.731518235771 3.7340398396 0.196988694120 682 4 141 2 [31]
144 0.267399364751 0.730000362776 3.7397246659 0.196863112878 692 3 142 2 [31]
145 0.267180209115 0.729183934272 3.7427921900 0.197419218947 701 2 143 2 [31]
146 0.266830522940 0.727882246299 3.7476971861 0.197483307621 700 4 144 2 [31]
147 0.266599301273 0.727022217829 3.7509475652 0.197975919605 701 5 145 2 [31]
148 0.266463244639 0.726516408869 3.7528628061 0.198814600421 689 7 146 2 [31]
149 0.266204712740 0.725555798359 3.7565075002 0.199188823733 666 13 147 2 [31]
150 0.266060086809 0.725018716184 3.7585494765 0.199981536709 696 12 148 2 [31]
151 0.265928773785 0.724531256064 3.7604054114 0.200818446150 708 10 149 2 [31]
152 0.265806218966 0.724076465458 3.7621392151 0.201682992527 757 1 150 2 [31]
153 0.265337223587 0.722337464496 3.7687889640 0.201225184047 728 5 150 3 [31]
154 0.265160470721 0.721682653575 3.7713011946 0.201866673945 734 5 152 2 [31]
155 0.264811017999 0.720388973399 3.7762779191 0.201842191275 737 4 152 3 [31]
156 0.264557254685 0.719450307642 3.7799001248 0.202172915766 748 4 154 2 [31]
157 0.264326445324 0.718597110482 3.7832007266 0.202582875054 754 6 154 3 [31]
158 0.264133558731 0.717884507074 3.7859634527 0.203130436010 739 6 155 3 [31]
159 0.263884354176 0.716964394584 3.7895388043 0.203453577882 763 14 156 3 [31]
160 0.263782902911 0.716589994864 3.7909962661 0.204339910716 767 14 157 3 [31]
161 0.263584558514 0.715858314926 3.7938489479 0.204845156062 799 4 158 3 [31]
162 0.263446936515 0.715350867643 3.7958308160 0.205579960523 724 12 160 2 [31]
163 0.262293004035 0.711103474603 3.8125302033 0.202358354812 782 4 160 3 [31]
164 0.261746242993 0.709095593510 3.8204941877 0.201486582897 795 2 161 3 [31]
165 0.261303051406 0.707470233641 3.8269740618 0.201004763986 802 1 162 3 [31]
166 0.260931614859 0.706109529524 3.8324217651 0.200789777410 803 2 163 3 [31]
167 0.260477794329 0.704448878834 3.8390988475 0.200248835720 810 1 164 3 [31]
168 0.260020018280 0.702775817464 3.8458577405 0.199683970772 785 12 166 2 [31]
169 0.259994751055 0.702683532112 3.8462314948 0.200774986693 794 11 167 2 [31]
170 0.259978680770 0.702624840702 3.8464692452 0.201900595380 770 13 168 2 [31]
171 0.259871832032 0.702234675774 3.8480507571 0.202671252259 775 13 169 2 [31]
172 0.258913905201 0.698741771079 3.8622877331 0.200126833155 838 4 170 2 [31]
173 0.258633027946 0.697719314982 3.8664822043 0.200200899695 824 5 171 2 [31]
174 0.258359199631 0.696723264153 3.8705801900 0.200294443153 837 4 172 2 [31]
175 0.257822270152 0.694772316073 3.8786408925 0.199360993450 848 3 173 2 [31]
176 0.257454234719 0.693436678941 3.8841854790 0.199073231479 851 3 174 2 [31]
177 0.257099022493 0.692148833498 3.8895519333 0.198827015476 865 2 173 4 [31]
178 0.256921982814 0.691507424179 3.8922321440 0.199262845396 874 174 4 [31]
179 0.256730966642 0.690815721145 3.8951280910 0.199638505952 882 175 4 [31]
180 0.256462891520 0.689845573530 3.8991995843 0.199707868948 877 1 176 4 [31]
181 0.256299052561 0.689252994618 3.9016921444 0.200176724553 892 177 4 [31]
182 0.256119396371 0.688603507395 3.9044290053 0.200578202937 900 178 4 [31]
183 0.255725905853 0.687182068714 3.9104368275 0.200135770767 890 3 179 4 [31]
184 0.255490382751 0.686331987745 3.9140416529 0.200304454563 898 2 182 2 [31]
185 0.255385508215 0.685953633813 3.9156489614 0.200980062477 901 2 183 2 [31]
186 0.255310071179 0.685681546904 3.9168059269 0.201768180518 910 2 184 2 [31]
187 0.255262257000 0.685509118879 3.9175395993 0.202663076465 914 2 185 2 [31]
188 0.255219692352 0.685355640398 3.9181929528 0.203577020282 911 2 186 2 [31]
189 0.255184182898 0.685227614770 3.9187381782 0.204517541780 921 2 187 2 [31]
190 0.255137263277 0.685058469697 3.9194588323 0.205410701048 927 2 188 2 [31]
191 0.255081879767 0.684858839753 3.9203098272 0.206267787896 931 2 189 2 [31]
192 0.255025413582 0.684655337864 3.9211778385 0.207118327957 913 7 190 2 [31]
193 0.254122149182 0.681404197492 3.9351154680 0.204536070039 928 5 191 2 [31]
194 0.253726383964 0.679982190210 3.9412535046 0.203999865115 944 3 192 2 [31]
195 0.253357072249 0.678656591611 3.9469985626 0.203563434750 923 8 193 2 [31]
196 0.253061024994 0.677594913271 3.9516160184 0.203414723735 960 2 194 2 [31]
197 0.252736646017 0.676432598146 3.9566877845 0.203145550891 943 6 193 4 [31]
198 0.252423833972 0.675312685029 3.9615910442 0.202916323113 964 3 193 5 [31]
199 0.252217943605 0.674576078546 3.9648249673 0.203110782212 978 1 194 5 [31]
200 0.251889762118 0.673402793768 3.9699906483 0.202806830083 982 1 195 5 [31]
201 0.251632953532 0.672485392615 3.9740422944 0.202783975597 988 1 195 6 [31]
202 0.251413113122 0.671700553480 3.9775172726 0.202904181929 981 2 196 6 [31]
203 0.251303222488 0.671308412260 3.9792565734 0.203463413364 1004 198 5 [31]
204 0.251067679111 0.670468270919 3.9829897800 0.203509275014 1000 2 199 5 [31]
205 0.250676007396 0.669072416926 3.9892130499 0.202916660206 1015 200 5 [31]
206 0.250493581732 0.668422779650 3.9921182534 0.203165627362 996 5 202 4 [31]
207 0.250232899836 0.667495012201 3.9962770709 0.203091800294 1005 4 203 4 [31]
208 0.249977554080 0.666586861340 4.0003591670 0.203033829823 1011 4 204 4 [31]
209 0.249723029123 0.665682244868 4.0044364491 0.202973461104 1024 2 202 7 [31]
210 0.249483197685 0.664830412632 4.0082859659 0.202967173623 1034 1 203 7 [31]
211 0.249234811305 0.663948768691 4.0122806070 0.202920517815 1042 204 7 [31]
212 0.248883089439 0.662701334345 4.0179507666 0.202447681085 1040 1 204 8 [31]
213 0.248648934166 0.661871515122 4.0217345124 0.202447590989 1050 204 9 [31]
214 0.248453655696 0.661179866229 4.0248954969 0.202600601123 1052 1 206 8 [31]
215 0.248326557473 0.660729895254 4.0269555145 0.203027234912 1059 1 206 9 [31]
216 0.248288059038 0.660593627714 4.0275799161 0.203813486591 1057 2 206 10 [31]
217 0.248139606440 0.660068301417 4.0299894658 0.204145673028 1074 207 10 [31]
218 0.247987770885 0.659531218467 4.0324569088 0.204459746374 1080 208 10 [31]
219 0.247700442597 0.658515454807 4.0371344900 0.204210480783 1085 209 10 [31]
220 0.247321498832 0.657176997745 4.0433201510 0.203578556061 1072 3 210 10 [31]
221 0.247136285103 0.656523299537 4.0463503754 0.203739316351 1081 2 211 10 [31]
222 0.246861326631 0.655553446823 4.0508572714 0.203525236110 1075 3 212 10 [31]
223 0.246567914673 0.654519284419 4.0556777281 0.203229932971 1091 213 10 [31]
224 0.246399437647 0.653925832745 4.0584508209 0.203444793453 1094 2 214 10 [31]
225 0.246186111325 0.653174782327 4.0619675684 0.203469941477 1106 215 10 [31]
226 0.245980808469 0.652452381136 4.0653578067 0.203523499732 1107 2 216 10 [31]
227 0.245760809998 0.651678706848 4.0689970057 0.203511523693 1113 2 217 10 [31]
228 0.245701829886 0.651471366683 4.0699737583 0.204162888593 1127 218 10 [31]
229 0.245565969478 0.650993882947 4.0722254884 0.204492033188 1127 1 219 10 [31]
230 0.245487983666 0.650719878150 4.0735191396 0.205059092013 1124 2 220 10 [31]
231 0.245350731323 0.650237776690 4.0757979184 0.205375561610 1124 1 221 10 [31]
232 0.245193741050 0.649686560340 4.0784075308 0.205605574168 1119 4 222 10 [31]
233 0.245009354534 0.649039444410 4.0814768150 0.205716559295 1141 1 223 10 [31]
234 0.244856361067 0.648502744227 4.0840270420 0.205955223951 1147 1 224 10 [31]
235 0.244537489283 0.647384842567 4.0893525280 0.205492088830 1145 2 225 10 [31]
236 0.244384036808 0.646847204698 4.0919202951 0.205719838467 1149 1 226 10 [31]
237 0.244248729930 0.646373323084 4.0941871030 0.206020253179 1154 1 227 10 [31]
238 0.244044252791 0.645657510223 4.0976174959 0.206024979567 1156 3 228 10 [31]
239 0.243865223930 0.645031101988 4.1006256812 0.206132876976 1174 230 9 [31]
240 0.243658199208 0.644307108117 4.1041097868 0.206118224383 1174 231 9 [31]
241 0.243494586189 0.643735211259 4.1068674899 0.206283072195 1182 232 9 [31]
242 0.243281864828 0.642992029715 4.1104584623 0.206235795742 1184 2 233 9 [31]
243 0.243097414286 0.642347955667 4.1135772790 0.206304153182 1185 3 233 10 [31]
244 0.242944272745 0.641813446484 4.1161702999 0.206501472520 1195 234 10 [31]
245 0.242812896716 0.641355077663 4.1183973896 0.206787762760 1193 3 235 10 [31]
246 0.242655357555 0.640805635785 4.1210711771 0.206959101161 1219 236 10 [31]
247 0.242417519488 0.639976572120 4.1251143981 0.206784017368 1216 1 237 10 [31]
248 0.242284860892 0.639514372584 4.1273730283 0.207053736330 1214 2 238 10 [31]
249 0.242114163015 0.638919877374 4.1302829522 0.207157338748 1215 4 239 10 [31]
250 0.241957298443 0.638373795951 4.1329606771 0.207316392243 1228 2 239 11 [31]
251 0.241783518678 0.637769092691 4.1359312060 0.207399253746 1235 1 239 12 [31]
252 0.241644570499 0.637285792647 4.1383094101 0.207627917484 1234 1 240 12 [31]
253 0.241437882296 0.636567201713 4.1418521008 0.207561875833 1252 241 12 [31]
254 0.241111109394 0.635431912046 4.1474654673 0.206975920721 1247 2 242 12 [31]
255 0.240927071388 0.634792948890 4.1506336098 0.206998971770 1264 246 9 [31]
256 0.240769429382 0.634245876548 4.1533512065 0.207131753980 1257 2 247 9 [31]
257 0.240564191091 0.633533968951 4.1568946545 0.207056100353 1258 3 248 9 [31]
258 0.240355545510 0.632810636843 4.1605031325 0.206961917431 1273 1 249 9 [31]
259 0.240220096944 0.632341276672 4.1628490402 0.207179343983 1272 2 250 9 [31]
260 0.240083111663 0.631866761610 4.1652242554 0.207386940276 1283 1 251 9 [31]
261 0.239973488367 0.631487151287 4.1671269889 0.207709724954 1235 12 252 9 [31]
262 0.239837425470 0.631016136563 4.1694910544 0.207915113346 1246 9 253 9 [31]
263 0.239663399332 0.630413948562 4.1725186357 0.207952584982 1245 11 254 9 [31]
264 0.239543424447 0.629998956279 4.1746084340 0.208221320309 1254 11 255 9 [31]
265 0.239431429856 0.629611685928 4.1765611165 0.208521898048 1255 11 256 9 [31]
266 0.239332402171 0.629269349330 4.1782892368 0.208876285537 1308 2 257 9 [31]
267 0.239193134553 0.628788054936 4.1807220005 0.209052233604 1273 9 258 9 [31]
268 0.239002544182 0.628129679948 4.1840558787 0.209000542892 1256 13 259 9 [31]
269 0.238812169486 0.627472379123 4.1873912965 0.208946234936 1249 16 260 9 [31]
270 0.238644375431 0.626893314320 4.1903355074 0.208987244199 1272 13 261 9 [31]
271 0.238536646493 0.626521671449 4.1922279646 0.209288245710 1281 12 262 9 [31]
272 0.238442500711 0.626196973790 4.1938832088 0.209646320094 1304 9 263 9 [31]
273 0.238342268099 0.625851371597 4.1956469072 0.209975191600 1295 11 264 9 [31]
274 0.238273822341 0.625615422784 4.1968521350 0.210441903538 1301 11 265 9 [31]
275 0.238204868340 0.625377764810 4.1980670125 0.210904506559 1306 10 266 9 [31]
276 0.238114015728 0.625064696407 4.1996687887 0.211268076750 1317 9 267 9 [31]
277 0.238000223854 0.624672687065 4.2016767203 0.211527383183 1316 10 268 9 [31]
278 0.237940127980 0.624465705954 4.2027379261 0.212023134205 1319 10 269 9 [31]
279 0.237888099334 0.624286536206 4.2036571094 0.212553267406 1320 12 270 9 [31]
280 0.237828084185 0.624079893919 4.2047178887 0.213046163816 1331 9 271 9 [31]
281 0.237722133547 0.623715167418 4.2065918940 0.213331219897 1341 9 272 9 [31]
282 0.237612474625 0.623337782208 4.2085332497 0.213597071910 1339 11 273 9 [31]
283 0.237520786887 0.623022327172 4.2101578270 0.213941261553 1355 9 274 9 [31]
284 0.237413225894 0.622652356310 4.2120652556 0.214211550940 1339 12 275 9 [31]
285 0.237303237026 0.622274142349 4.2140175268 0.214468331000 1344 13 276 9 [31]
286 0.237240345105 0.622057927638 4.2151346541 0.214935805197 1363 10 277 9 [31]
287 0.237125403248 0.621662863747 4.2171778574 0.215165337445 1361 10 278 9 [31]
288 0.237030741013 0.621337591839 4.2188620587 0.215484411908 1365 11 279 9 [31]
289 0.236910936782 0.620926044421 4.2209955082 0.215686713394 1385 9 280 9 [31]
290 0.236851694525 0.620722585180 4.2220512798 0.216162561872 1376 11 281 9 [31]
291 0.236735010693 0.620321943256 4.2241322780 0.216374182974 1393 9 282 9 [31]
292 0.236575378237 0.619774032676 4.2269825687 0.216386701625 1399 9 283 9 [31]
293 0.236382527452 0.619112411515 4.2304311185 0.216244205993 1402 10 284 9 [31]
294 0.236270160444 0.618727063437 4.2324430564 0.216467006551 1408 10 285 9 [31]
295 0.236104828070 0.618160283625 4.2354068241 0.216444400991 1409 9 286 9 [31]
296 0.235878480738 0.617384734736 4.2394710907 0.216139090908 1403 11 287 9 [31]
297 0.235709988643 0.616807717334 4.2425015832 0.216095828820 1417 10 288 9 [31]
298 0.235407648397 0.615772961640 4.2479503398 0.215436412715 1424 10 289 9 [31]
299 0.235117208585 0.614779705398 4.2531978243 0.214829181173 1429 10 290 9 [31]
300 0.234892444467 0.614011566788 4.2572676285 0.214519359849 1438 9 291 9 [31]



History of updates

Please note that the results are taken from a running search. For updates look at the list below.

01-Aug-2025: First presentation for N=2–300 by E. Specht [31].


References

[2]   N. J. A. Sloane, with collaboration of R. H. Hardin, W. D. Smith, and others, Tables of Spherical Codes, http://neilsloane.com/packings/dim4, 1994.
[31]   , program hsp5, September 2010–August 2025.