N | radius | ratio | density | contacts | loose | boundary | symmetry group | reference |
---|---|---|---|---|---|---|---|---|
1 | 0.809016994375 | 1.2360679775 | 0.864806265977 | 5 | 1 | C3 | ||
2 | 0.437152698242 | 2.2875302017 | 0.505009863813 | 5 | 2 | D1 | ||
3 | 0.389795792433 | 2.5654458550 | 0.602280894881 | 7 | 3 | D1 | [1] | |
4 | 0.354680462504 | 2.8194392015 | 0.664872028015 | 9 | 4 | D1 | [1] | |
5 | 0.340440645254 | 2.9373695942 | 0.765695954932 | 15 | 5 | [1] | ||
6 | 0.309016994375 | 3.2360679775 | 0.757041202686 | 15 | 5 | [1] | ||
7 | 0.277511095117 | 3.6034595286 | 0.712298912009 | 13 | 1 | 5 | D1 | [1] |
8 | 0.257541824500 | 3.8828644704 | 0.701114681674 | 15 | 1 | 7 | D1 | [1] |
9 | 0.243640224399 | 4.1044125717 | 0.705901377804 | 17 | 1 | 6 | D1 | [1] |
10 | 0.230721507966 | 4.3342296469 | 0.703363296033 | 17 | 2 | 5 | [2] | |
11 | 0.224333593340 | 4.4576471366 | 0.731450345446 | 21 | 1 | 7 | [1] | |
12 | 0.217384640521 | 4.6001410109 | 0.749277161807 | 27 | 9 | D1 | [1] | |
13 | 0.207999994722 | 4.8076924297 | 0.743144963272 | 25 | 1 | 8 | [2] | |
14 | 0.202386816023 | 4.9410333126 | 0.757697772154 | 25 | 2 | 7 | [1] | |
15 | 0.197735768366 | 5.0572539721 | 0.774934987330 | 35 | 10 | [1] | ||
16 | 0.191785609135 | 5.2141555590 | 0.777598749710 | 40 | 10 | [1] | ||
17 | 0.183126736787 | 5.4606990631 | 0.753279195582 | 31 | 2 | 10 | D1 | [2] |
18 | 0.178473321196 | 5.6030783385 | 0.757569801809 | 35 | 1 | 10 | D1 | [2] |
19 | 0.173441904330 | 5.7656193517 | 0.755205607498 | 37 | 1 | 11 | [1] | |
20 | 0.169279411749 | 5.9073929291 | 0.757254419213 | 41 | 11 | [2] | ||
21 | 0.165404018640 | 6.0458023222 | 0.759127889229 | 50 | 10 | [2] | ||
22 | 0.161673301786 | 6.1853131528 | 0.759806203277 | 45 | 12 | [2] | ||
23 | 0.158923367389 | 6.2923408711 | 0.767550381308 | 47 | 11 | [1] | ||
24 | 0.156027298450 | 6.4091348753 | 0.771997613946 | 41 | 4 | 10 | [1] | |
25 | 0.153122210789 | 6.5307312038 | 0.774497337032 | 47 | 2 | 12 | [1] | |
26 | 0.150683336700 | 6.6364338745 | 0.780022883175 | 45 | 4 | 12 | [2] | |
27 | 0.148137584795 | 6.7504813271 | 0.782884729566 | 47 | 4 | 11 | [1] | |
28 | 0.145444423784 | 6.8754784404 | 0.782628611099 | 53 | 2 | 13 | [1] | |
29 | 0.143333013135 | 6.9767597717 | 0.787216154549 | 53 | 3 | 13 | [1] | |
30 | 0.141698173815 | 7.0572539721 | 0.795890460898 | 70 | 15 | [2] | ||
31 | 0.138616362210 | 7.2141555590 | 0.787035327241 | 70 | 15 | [1] | ||
32 | 0.135793611068 | 7.3641167072 | 0.779672455391 | 66 | 1 | 15 | [1] | |
33 | 0.134134799538 | 7.4551868974 | 0.784513474860 | 63 | 2 | 14 | [1] | |
34 | 0.131960534658 | 7.5780232521 | 0.782295061266 | 66 | 1 | 17 | [1] | |
35 | 0.130170592942 | 7.6822266642 | 0.783605271724 | 67 | 3 | 16 | [2] | |
36 | 0.128215138245 | 7.7993910367 | 0.781960200280 | 70 | 2 | 17 | [2] | |
37 | 0.126679668746 | 7.8939265464 | 0.784547243181 | 77 | 1 | 18 | [2] | |
38 | 0.125056798044 | 7.9963665762 | 0.785238789166 | 75 | 1 | 16 | [2] | |
39 | 0.124185741467 | 8.0524542366 | 0.794715374348 | 77 | 1 | 16 | [2] | |
40 | 0.122413791780 | 8.1690141728 | 0.791998265961 | 80 | 1 | 17 | [2] | |
41 | 0.120982726955 | 8.2656427506 | 0.792928693410 | 80 | 2 | 15 | [2] | |
42 | 0.119848964213 | 8.3438351476 | 0.797115765780 | 81 | 3 | 15 | [1] | |
43 | 0.118421345534 | 8.4444235580 | 0.796768171019 | 87 | 3 | 16 | D1 | [1] |
44 | 0.117257562843 | 8.5282345612 | 0.799351771065 | 85 | 3 | 17 | [1] | |
45 | 0.115792923917 | 8.6361063023 | 0.797223502406 | 84 | 4 | 16 | [1] | |
46 | 0.114685668831 | 8.7194852695 | 0.799428585597 | 80 | 7 | 14 | [2] | |
47 | 0.113728619203 | 8.7928615242 | 0.803231865120 | 93 | 3 | 18 | [2] | |
48 | 0.112997340346 | 8.8497658169 | 0.809806426252 | 92 | 2 | 18 | [1] |
01-Dec-2020: | First complete presentation from N=1 to N=48 by E. Specht [1].
The symmetry groups are still wrong and have to be corrected.
|
04-Dec-2020: | Only one day after the unexpected publication of packings in hexagonal containers, Paolo Amore (Universidad de Colima, Mexico) sent me packings from his own repository which improve my result for several values of N: 10, 13, 17, 18, 20, 21, 22, 26, 30, 35, 36, 37, 38, 39, 40, 41, 46, and 47. Among them are two packings which show a reflection symmetry like N = 17 and 18. |
[1] | ![]() |
[2] | ![]() |