トムソン問題
現在までに知られている最良の結果

| N |  E_{1} | 対称性 |  \left|\sum \mathbf {r} _{i}\right| |  v_{3} |  v_{4} |  v_{5} |  v_{6} |  v_{7} |  v_{8} |  e |  f_{3} |  f_{4} |  \theta _{1} | 対応する多面体 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 2 | 0.500000000 |  D_{\infty h} | 0 | – | – | – | – | – | – | 1 | – | – | 180.000° | 二角形 |
| 3 | 1.732050808 |  D_{3h} | 0 | – | – | – | – | – | – | 3 | 1 | – | 120.000° | 三角形 |
| 4 | 3.674234614 |  T_{d} | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 6 | 4 | 0 | 109.471° | 四面体 |
| 5 | 6.474691495 |  D_{3h} | 0 | 2 | 3 | 0 | 0 | 0 | 0 | 9 | 6 | 0 | 90.000° | 双三角錐 |
| 6 | 9.985281374 |  O_{h} | 0 | 0 | 6 | 0 | 0 | 0 | 0 | 12 | 8 | 0 | 90.000° | 八面体 |
| 7 | 14.452977414 |  D_{5h} | 0 | 0 | 5 | 2 | 0 | 0 | 0 | 15 | 10 | 0 | 72.000° | 双五角錐 |
| 8 | 19.675287861 |  D_{4d} | 0 | 0 | 8 | 0 | 0 | 0 | 0 | 16 | 8 | 2 | 71.694° | 反四角柱形（英語版） |
| 9 | 25.759986531 |  D_{3h} | 0 | 0 | 3 | 6 | 0 | 0 | 0 | 21 | 14 | 0 | 69.190° | 三側錐三角柱 |
| 10 | 32.716949460 |  D_{4d} | 0 | 0 | 2 | 8 | 0 | 0 | 0 | 24 | 16 | 0 | 64.996° | 双四角錐反柱 |
| 11 | 40.596450510 |  C_{2v} | 0.013219635 | 0 | 2 | 8 | 1 | 0 | 0 | 27 | 18 | 0 | 58.540° | edge-contracted icosahedron（英語版） |
| 12 | 49.165253058 |  I_{h} | 0 | 0 | 0 | 12 | 0 | 0 | 0 | 30 | 20 | 0 | 63.435° | 正二十面体 |
| 13 | 58.853230612 |  C_{2v} | 0.008820367 | 0 | 1 | 10 | 2 | 0 | 0 | 33 | 22 | 0 | 52.317° |  |
| 14 | 69.306363297 |  D_{6d} | 0 | 0 | 0 | 12 | 2 | 0 | 0 | 36 | 24 | 0 | 52.866° | gyroelongated hexagonal dipyramid |
| 15 | 80.670244114 |  D_{3} | 0 | 0 | 0 | 12 | 3 | 0 | 0 | 39 | 26 | 0 | 49.225° |  |
| 16 | 92.911655302 |  T | 0 | 0 | 0 | 12 | 4 | 0 | 0 | 42 | 28 | 0 | 48.936° |  |
| 17 | 106.050404829 |  D_{5h} | 0 | 0 | 0 | 12 | 5 | 0 | 0 | 45 | 30 | 0 | 50.108° |  |
| 18 | 120.084467447 |  D_{4d} | 0 | 0 | 2 | 8 | 8 | 0 | 0 | 48 | 32 | 0 | 47.534° |  |
| 19 | 135.089467557 |  C_{2v} | 0.000135163 | 0 | 0 | 14 | 5 | 0 | 0 | 50 | 32 | 1 | 44.910° |  |
| 20 | 150.881568334 |  D_{3h} | 0 | 0 | 0 | 12 | 8 | 0 | 0 | 54 | 36 | 0 | 46.093° |  |
| 21 | 167.641622399 |  C_{2v} | 0.001406124 | 0 | 1 | 10 | 10 | 0 | 0 | 57 | 38 | 0 | 44.321° |  |
| 22 | 185.287536149 |  T_{d} | 0 | 0 | 0 | 12 | 10 | 0 | 0 | 60 | 40 | 0 | 43.302° |  |
| 23 | 203.930190663 |  D_{3} | 0 | 0 | 0 | 12 | 11 | 0 | 0 | 63 | 42 | 0 | 41.481° |  |
| 24 | 223.347074052 |  O | 0 | 0 | 0 | 24 | 0 | 0 | 0 | 60 | 32 | 6 | 42.065° | 変形立方体 |
| 25 | 243.812760299 |  C_{s} | 0.001021305 | 0 | 0 | 14 | 11 | 0 | 0 | 68 | 44 | 1 | 39.610° |  |
| 26 | 265.133326317 |  C_{2} | 0.001919065 | 0 | 0 | 12 | 14 | 0 | 0 | 72 | 48 | 0 | 38.842° |  |
| 27 | 287.302615033 |  D_{5h} | 0 | 0 | 0 | 12 | 15 | 0 | 0 | 75 | 50 | 0 | 39.940° |  |
| 28 | 310.491542358 |  T | 0 | 0 | 0 | 12 | 16 | 0 | 0 | 78 | 52 | 0 | 37.824° |  |
| 29 | 334.634439920 |  D_{3} | 0 | 0 | 0 | 12 | 17 | 0 | 0 | 81 | 54 | 0 | 36.391° |  |
| 30 | 359.603945904 |  D_{2} | 0 | 0 | 0 | 12 | 18 | 0 | 0 | 84 | 56 | 0 | 36.942° |  |
| 31 | 385.530838063 |  C_{3v} | 0.003204712 | 0 | 0 | 12 | 19 | 0 | 0 | 87 | 58 | 0 | 36.373° |  |
| 32 | 412.261274651 |  I_{h} | 0 | 0 | 0 | 12 | 20 | 0 | 0 | 90 | 60 | 0 | 37.377° |  |
| 33 | 440.204057448 |  C_{s} | 0.004356481 | 0 | 0 | 15 | 17 | 1 | 0 | 92 | 60 | 1 | 33.700° |  |
| 34 | 468.904853281 |  D_{2} | 0 | 0 | 0 | 12 | 22 | 0 | 0 | 96 | 64 | 0 | 33.273° |  |
| 35 | 498.569872491 |  C_{2} | 0.000419208 | 0 | 0 | 12 | 23 | 0 | 0 | 99 | 66 | 0 | 33.100° |  |
| 36 | 529.122408375 |  D_{2} | 0 | 0 | 0 | 12 | 24 | 0 | 0 | 102 | 68 | 0 | 33.229° |  |
| 37 | 560.618887731 |  D_{5h} | 0 | 0 | 0 | 12 | 25 | 0 | 0 | 105 | 70 | 0 | 32.332° |  |
| 38 | 593.038503566 |  D_{6d} | 0 | 0 | 0 | 12 | 26 | 0 | 0 | 108 | 72 | 0 | 33.236° |  |
| 39 | 626.389009017 |  D_{3h} | 0 | 0 | 0 | 12 | 27 | 0 | 0 | 111 | 74 | 0 | 32.053° |  |
| 40 | 660.675278835 |  T_{d} | 0 | 0 | 0 | 12 | 28 | 0 | 0 | 114 | 76 | 0 | 31.916° |  |
| 41 | 695.916744342 |  D_{3h} | 0 | 0 | 0 | 12 | 29 | 0 | 0 | 117 | 78 | 0 | 31.528° |  |
| 42 | 732.078107544 |  D_{5h} | 0 | 0 | 0 | 12 | 30 | 0 | 0 | 120 | 80 | 0 | 31.245° |  |
| 43 | 769.190846459 |  C_{2v} | 0.000399668 | 0 | 0 | 12 | 31 | 0 | 0 | 123 | 82 | 0 | 30.867° |  |
| 44 | 807.174263085 |  O_{h} | 0 | 0 | 0 | 24 | 20 | 0 | 0 | 120 | 72 | 6 | 31.258° |  |
| 45 | 846.188401061 |  D_{3} | 0 | 0 | 0 | 12 | 33 | 0 | 0 | 129 | 86 | 0 | 30.207° |  |
| 46 | 886.167113639 |  T | 0 | 0 | 0 | 12 | 34 | 0 | 0 | 132 | 88 | 0 | 29.790° |  |
| 47 | 927.059270680 |  C_{s} | 0.002482914 | 0 | 0 | 14 | 33 | 0 | 0 | 134 | 88 | 1 | 28.787° |  |
| 48 | 968.713455344 |  O | 0 | 0 | 0 | 24 | 24 | 0 | 0 | 132 | 80 | 6 | 29.690° |  |
| 49 | 1011.557182654 |  C_{3} | 0.001529341 | 0 | 0 | 12 | 37 | 0 | 0 | 141 | 94 | 0 | 28.387° |  |
| 50 | 1055.182314726 |  D_{6d} | 0 | 0 | 0 | 12 | 38 | 0 | 0 | 144 | 96 | 0 | 29.231° |  |
| 51 | 1099.819290319 |  D_{3} | 0 | 0 | 0 | 12 | 39 | 0 | 0 | 147 | 98 | 0 | 28.165° |  |
| 52 | 1145.418964319 |  C_{3} | 0.000457327 | 0 | 0 | 12 | 40 | 0 | 0 | 150 | 100 | 0 | 27.670° |  |
| 53 | 1191.922290416 |  C_{2v} | 0.000278469 | 0 | 0 | 18 | 35 | 0 | 0 | 150 | 96 | 3 | 27.137° |  |
| 54 | 1239.361474729 |  C_{2} | 0.000137870 | 0 | 0 | 12 | 42 | 0 | 0 | 156 | 104 | 0 | 27.030° |  |
| 55 | 1287.772720783 |  C_{2} | 0.000391696 | 0 | 0 | 12 | 43 | 0 | 0 | 159 | 106 | 0 | 26.615° |  |
| 56 | 1337.094945276 |  D_{2} | 0 | 0 | 0 | 12 | 44 | 0 | 0 | 162 | 108 | 0 | 26.683° |  |
| 57 | 1387.383229253 |  D_{3} | 0 | 0 | 0 | 12 | 45 | 0 | 0 | 165 | 110 | 0 | 26.702° |  |
| 58 | 1438.618250640 |  D_{2} | 0 | 0 | 0 | 12 | 46 | 0 | 0 | 168 | 112 | 0 | 26.155° |  |
| 59 | 1490.773335279 |  C_{2} | 0.000154286 | 0 | 0 | 14 | 43 | 2 | 0 | 171 | 114 | 0 | 26.170° |  |
| 60 | 1543.830400976 |  D_{3} | 0 | 0 | 0 | 12 | 48 | 0 | 0 | 174 | 116 | 0 | 25.958° |  |
| 61 | 1597.941830199 |  C_{1} | 0.001091717 | 0 | 0 | 12 | 49 | 0 | 0 | 177 | 118 | 0 | 25.392° |  |
| 62 | 1652.909409898 |  D_{5} | 0 | 0 | 0 | 12 | 50 | 0 | 0 | 180 | 120 | 0 | 25.880° |  |
| 63 | 1708.879681503 |  D_{3} | 0 | 0 | 0 | 12 | 51 | 0 | 0 | 183 | 122 | 0 | 25.257° |  |
| 64 | 1765.802577927 |  D_{2} | 0 | 0 | 0 | 12 | 52 | 0 | 0 | 186 | 124 | 0 | 24.920° |  |
| 65 | 1823.667960264 |  C_{2} | 0.000399515 | 0 | 0 | 12 | 53 | 0 | 0 | 189 | 126 | 0 | 24.527° |  |
| 66 | 1882.441525304 |  C_{2} | 0.000776245 | 0 | 0 | 12 | 54 | 0 | 0 | 192 | 128 | 0 | 24.765° |  |
| 67 | 1942.122700406 |  D_{5} | 0 | 0 | 0 | 12 | 55 | 0 | 0 | 195 | 130 | 0 | 24.727° |  |
| 68 | 2002.874701749 |  D_{2} | 0 | 0 | 0 | 12 | 56 | 0 | 0 | 198 | 132 | 0 | 24.433° |  |
| 69 | 2064.533483235 |  D_{3} | 0 | 0 | 0 | 12 | 57 | 0 | 0 | 201 | 134 | 0 | 24.137° |  |
| 70 | 2127.100901551 |  D_{2d} | 0 | 0 | 0 | 12 | 50 | 0 | 0 | 200 | 128 | 4 | 24.291° |  |
| 71 | 2190.649906425 |  C_{2} | 0.001256769 | 0 | 0 | 14 | 55 | 2 | 0 | 207 | 138 | 0 | 23.803° |  |
| 72 | 2255.001190975 |  I | 0 | 0 | 0 | 12 | 60 | 0 | 0 | 210 | 140 | 0 | 24.492° |  |
| 73 | 2320.633883745 |  C_{2} | 0.001572959 | 0 | 0 | 12 | 61 | 0 | 0 | 213 | 142 | 0 | 22.810° |  |
| 74 | 2387.072981838 |  C_{2} | 0.000641539 | 0 | 0 | 12 | 62 | 0 | 0 | 216 | 144 | 0 | 22.966° |  |
| 75 | 2454.369689040 |  D_{3} | 0 | 0 | 0 | 12 | 63 | 0 | 0 | 219 | 146 | 0 | 22.736° |  |
| 76 | 2522.674871841 |  C_{2} | 0.000943474 | 0 | 0 | 12 | 64 | 0 | 0 | 222 | 148 | 0 | 22.886° |  |
| 77 | 2591.850152354 |  D_{5} | 0 | 0 | 0 | 12 | 65 | 0 | 0 | 225 | 150 | 0 | 23.286° |  |
| 78 | 2662.046474566 |  T_{h} | 0 | 0 | 0 | 12 | 66 | 0 | 0 | 228 | 152 | 0 | 23.426° |  |
| 79 | 2733.248357479 |  C_{s} | 0.000702921 | 0 | 0 | 12 | 63 | 1 | 0 | 230 | 152 | 1 | 22.636° |  |
| 80 | 2805.355875981 |  D_{4d} | 0 | 0 | 0 | 16 | 64 | 0 | 0 | 232 | 152 | 2 | 22.778° |  |
| 81 | 2878.522829664 |  C_{2} | 0.000194289 | 0 | 0 | 12 | 69 | 0 | 0 | 237 | 158 | 0 | 21.892° |  |
| 82 | 2952.569675286 |  D_{2} | 0 | 0 | 0 | 12 | 70 | 0 | 0 | 240 | 160 | 0 | 22.206° |  |
| 83 | 3027.528488921 |  C_{2} | 0.000339815 | 0 | 0 | 14 | 67 | 2 | 0 | 243 | 162 | 0 | 21.646° |  |
| 84 | 3103.465124431 |  C_{2} | 0.000401973 | 0 | 0 | 12 | 72 | 0 | 0 | 246 | 164 | 0 | 21.513° |  |
| 85 | 3180.361442939 |  C_{2} | 0.000416581 | 0 | 0 | 12 | 73 | 0 | 0 | 249 | 166 | 0 | 21.498° |  |
| 86 | 3258.211605713 |  C_{2} | 0.001378932 | 0 | 0 | 12 | 74 | 0 | 0 | 252 | 168 | 0 | 21.522° |  |
| 87 | 3337.000750014 |  C_{2} | 0.000754863 | 0 | 0 | 12 | 75 | 0 | 0 | 255 | 170 | 0 | 21.456° |  |
| 88 | 3416.720196758 |  D_{2} | 0 | 0 | 0 | 12 | 76 | 0 | 0 | 258 | 172 | 0 | 21.486° |  |
| 89 | 3497.439018625 |  C_{2} | 0.000070891 | 0 | 0 | 12 | 77 | 0 | 0 | 261 | 174 | 0 | 21.182° |  |
| 90 | 3579.091222723 |  D_{3} | 0 | 0 | 0 | 12 | 78 | 0 | 0 | 264 | 176 | 0 | 21.230° |  |
| 91 | 3661.713699320 |  C_{2} | 0.000033221 | 0 | 0 | 12 | 79 | 0 | 0 | 267 | 178 | 0 | 21.105° |  |
| 92 | 3745.291636241 |  D_{2} | 0 | 0 | 0 | 12 | 80 | 0 | 0 | 270 | 180 | 0 | 21.026° |  |
| 93 | 3829.844338421 |  C_{2} | 0.000213246 | 0 | 0 | 12 | 81 | 0 | 0 | 273 | 182 | 0 | 20.751° |  |
| 94 | 3915.309269620 |  D_{2} | 0 | 0 | 0 | 12 | 82 | 0 | 0 | 276 | 184 | 0 | 20.952° |  |
| 95 | 4001.771675565 |  C_{2} | 0.000116638 | 0 | 0 | 12 | 83 | 0 | 0 | 279 | 186 | 0 | 20.711° |  |
| 96 | 4089.154010060 |  C_{2} | 0.000036310 | 0 | 0 | 12 | 84 | 0 | 0 | 282 | 188 | 0 | 20.687° |  |
| 97 | 4177.533599622 |  C_{2} | 0.000096437 | 0 | 0 | 12 | 85 | 0 | 0 | 285 | 190 | 0 | 20.450° |  |
| 98 | 4266.822464156 |  C_{2} | 0.000112916 | 0 | 0 | 12 | 86 | 0 | 0 | 288 | 192 | 0 | 20.422° |  |
| 99 | 4357.139163132 |  C_{2} | 0.000156508 | 0 | 0 | 12 | 87 | 0 | 0 | 291 | 194 | 0 | 20.284° |  |
| 100 | 4448.350634331 |  T | 0 | 0 | 0 | 12 | 88 | 0 | 0 | 294 | 196 | 0 | 20.297° |  |
| 101 | 4540.590051694 |  D_{3} | 0 | 0 | 0 | 12 | 89 | 0 | 0 | 297 | 198 | 0 | 20.011° |  |
| 102 | 4633.736565899 |  D_{3} | 0 | 0 | 0 | 12 | 90 | 0 | 0 | 300 | 200 | 0 | 20.040° |  |
| 103 | 4727.836616833 |  C_{2} | 0.000201245 | 0 | 0 | 12 | 91 | 0 | 0 | 303 | 202 | 0 | 19.907° |  |
| 104 | 4822.876522746 |  D_{6} | 0 | 0 | 0 | 12 | 92 | 0 | 0 | 306 | 204 | 0 | 19.957° |  |
| 105 | 4919.000637616 |  D_{3} | 0 | 0 | 0 | 12 | 93 | 0 | 0 | 309 | 206 | 0 | 19.842° |  |
| 106 | 5015.984595705 |  D_{2} | 0 | 0 | 0 | 12 | 94 | 0 | 0 | 312 | 208 | 0 | 19.658° |  |
| 107 | 5113.953547724 |  C_{2} | 0.000064137 | 0 | 0 | 12 | 95 | 0 | 0 | 315 | 210 | 0 | 19.327° |  |
| 108 | 5212.813507831 |  C_{2} | 0.000432525 | 0 | 0 | 12 | 96 | 0 | 0 | 318 | 212 | 0 | 19.327° |  |
| 109 | 5312.735079920 |  C_{2} | 0.000647299 | 0 | 0 | 14 | 93 | 2 | 0 | 321 | 214 | 0 | 19.103° |  |
| 110 | 5413.549294192 |  D_{6} | 0 | 0 | 0 | 12 | 98 | 0 | 0 | 324 | 216 | 0 | 19.476° |  |
| 111 | 5515.293214587 |  D_{3} | 0 | 0 | 0 | 12 | 99 | 0 | 0 | 327 | 218 | 0 | 19.255° |  |
| 112 | 5618.044882327 |  D_{5} | 0 | 0 | 0 | 12 | 100 | 0 | 0 | 330 | 220 | 0 | 19.351° |  |
| 113 | 5721.824978027 |  D_{3} | 0 | 0 | 0 | 12 | 101 | 0 | 0 | 333 | 222 | 0 | 18.978° |  |
| 114 | 5826.521572163 |  C_{2} | 0.000149772 | 0 | 0 | 12 | 102 | 0 | 0 | 336 | 224 | 0 | 18.836° |  |
| 115 | 5932.181285777 |  C_{3} | 0.000049972 | 0 | 0 | 12 | 103 | 0 | 0 | 339 | 226 | 0 | 18.458° |  |
| 116 | 6038.815593579 |  C_{2} | 0.000259726 | 0 | 0 | 12 | 104 | 0 | 0 | 342 | 228 | 0 | 18.386° |  |
| 117 | 6146.342446579 |  C_{2} | 0.000127609 | 0 | 0 | 12 | 105 | 0 | 0 | 345 | 230 | 0 | 18.566° |  |
| 118 | 6254.877027790 |  C_{2} | 0.000332475 | 0 | 0 | 12 | 106 | 0 | 0 | 348 | 232 | 0 | 18.455° |  |
| 119 | 6364.347317479 |  C_{2} | 0.000685590 | 0 | 0 | 12 | 107 | 0 | 0 | 351 | 234 | 0 | 18.336° |  |
| 120 | 6474.756324980 |  C_{s} | 0.001373062 | 0 | 0 | 12 | 108 | 0 | 0 | 354 | 236 | 0 | 18.418° |  |
| 121 | 6586.121949584 |  C_{3} | 0.000838863 | 0 | 0 | 12 | 109 | 0 | 0 | 357 | 238 | 0 | 18.199° |  |
| 122 | 6698.374499261 |  I_{h} | 0 | 0 | 0 | 12 | 110 | 0 | 0 | 360 | 240 | 0 | 18.612° |  |
| 123 | 6811.827228174 |  C_{2v} | 0.001939754 | 0 | 0 | 14 | 107 | 2 | 0 | 363 | 242 | 0 | 17.840° |  |
| 124 | 6926.169974193 |  D_{2} | 0 | 0 | 0 | 12 | 112 | 0 | 0 | 366 | 244 | 0 | 18.111° |  |
| 125 | 7041.473264023 |  C_{2} | 0.000088274 | 0 | 0 | 12 | 113 | 0 | 0 | 369 | 246 | 0 | 17.867° |  |
| 126 | 7157.669224867 |  D_{4} | 0 | 0 | 2 | 16 | 100 | 8 | 0 | 372 | 248 | 0 | 17.920° |  |
| 127 | 7274.819504675 |  D_{5} | 0 | 0 | 0 | 12 | 115 | 0 | 0 | 375 | 250 | 0 | 17.877° |  |
| 128 | 7393.007443068 |  C_{2} | 0.000054132 | 0 | 0 | 12 | 116 | 0 | 0 | 378 | 252 | 0 | 17.814° |  |
| 129 | 7512.107319268 |  C_{2} | 0.000030099 | 0 | 0 | 12 | 117 | 0 | 0 | 381 | 254 | 0 | 17.743° |  |
| 130 | 7632.167378912 |  C_{2} | 0.000025622 | 0 | 0 | 12 | 118 | 0 | 0 | 384 | 256 | 0 | 17.683° |  |
| 131 | 7753.205166941 |  C_{2} | 0.000305133 | 0 | 0 | 12 | 119 | 0 | 0 | 387 | 258 | 0 | 17.511° |  |
| 132 | 7875.045342797 |  I | 0 | 0 | 0 | 12 | 120 | 0 | 0 | 390 | 260 | 0 | 17.958° |  |
| 133 | 7998.179212898 |  C_{3} | 0.000591438 | 0 | 0 | 12 | 121 | 0 | 0 | 393 | 262 | 0 | 17.133° |  |
| 134 | 8122.089721194 |  C_{2} | 0.000470268 | 0 | 0 | 12 | 122 | 0 | 0 | 396 | 264 | 0 | 17.214° |  |
| 135 | 8246.909486992 |  D_{3} | 0 | 0 | 0 | 12 | 123 | 0 | 0 | 399 | 266 | 0 | 17.431° |  |