Fullerenes are cubic plane graphs where all faces are pentagons or hexagons. Euler's formula implies that each fullerene contains exactly 12 pentagonal faces. The dual graph of a fullerene is a triangulation where all vertices have degree 5 or 6.
The fullerene lists are currently only available in 'planar_code' format. The larger files are compressed with gzip.
The following lists are available:
All numbers up to 380 vertices were independently confirmed by fullgen and buckygen. The fullerenes with more than 380 vertices were generated with buckygen.
The fullerenes in the downloadable lists from the "Fullerenes"-table are sorted according to their lexicographically minimal spiral development. So the order in which they appear is the same as in the Atlas of Fullerenes [1]. More information about spirals in fullerenes can be found in [2].
| Vertices | Faces | Fullerenes | IPR Fullerenes |
|---|---|---|---|
| 20 | 12 | 1 | 0 |
| 22 | 13 | 0 | 0 |
| 24 | 14 | 1 | 0 |
| 26 | 15 | 1 | 0 |
| 28 | 16 | 2 | 0 |
| 30 | 17 | 3 | 0 |
| 32 | 18 | 6 | 0 |
| 34 | 19 | 6 | 0 |
| 36 | 20 | 15 | 0 |
| 38 | 21 | 17 | 0 |
| 40 | 22 | 40 | 0 |
| 42 | 23 | 45 | 0 |
| 44 | 24 | 89 | 0 |
| 46 | 25 | 116 | 0 |
| 48 | 26 | 199 | 0 |
| 50 | 27 | 271 | 0 |
| 52 | 28 | 437 | 0 |
| 54 | 29 | 580 | 0 |
| 56 | 30 | 924 | 0 |
| 58 | 31 | 1205 | 0 |
| 60 | 32 | 1812 | 1 |
| 62 | 33 | 2385 | 0 |
| 64 | 34 | 3465 | 0 |
| 66 | 35 | 4478 | 0 |
| 68 | 36 | 6332 | 0 |
| 70 | 37 | 8149 | 1 |
| 72 | 38 | 11190 | 1 |
| 74 | 39 | 14246 | 1 |
| 76 | 40 | 19151 | 2 |
| 78 | 41 | 24109 | 5 |
| 80 | 42 | 31924 | 7 |
| 82 | 43 | 39718 | 9 |
| 84 | 44 | 51592 | 24 |
| 86 | 45 | 63761 | 19 |
| 88 | 46 | 81738 | 35 |
| 90 | 47 | 99918 | 46 |
| 92 | 48 | 126409 | 86 |
| 94 | 49 | 153493 | 134 |
| 96 | 50 | 191839 | 187 |
| 98 | 51 | 231017 | 259 |
| 100 | 52 | 285914 | 450 |
| 102 | 53 | 341658 | 616 |
| 104 | 54 | 419013 | 823 |
| 106 | 55 | 497529 | 1233 |
| 108 | 56 | 604217 | 1799 |
| 110 | 57 | 713319 | 2355 |
| 112 | 58 | 860161 | 3342 |
| 114 | 59 | 1008444 | 4468 |
| 116 | 60 | 1207119 | 6063 |
| 118 | 61 | 1408553 | 8148 |
| 120 | 62 | 1674171 | 10774 |
| 122 | 63 | 1942929 | 13977 |
| 124 | 64 | 2295721 | 18769 |
| 126 | 65 | 2650866 | 23589 |
| 128 | 66 | 3114236 | 30683 |
| 130 | 67 | 3580637 | 39393 |
| 132 | 68 | 4182071 | 49878 |
| 134 | 69 | 4787715 | 62372 |
| 136 | 70 | 5566949 | 79362 |
| 138 | 71 | 6344698 | 98541 |
| 140 | 72 | 7341204 | 121354 |
| 142 | 73 | 8339033 | 151201 |
| 144 | 74 | 9604411 | 186611 |
| 146 | 75 | 10867631 | 225245 |
| 148 | 76 | 12469092 | 277930 |
| 150 | 77 | 14059174 | 335569 |
| 152 | 78 | 16066025 | 404667 |
| 154 | 79 | 18060979 | 489646 |
| 156 | 80 | 20558767 | 586264 |
| 158 | 81 | 23037594 | 697720 |
| 160 | 82 | 26142839 | 836497 |
| 162 | 83 | 29202543 | 989495 |
| 164 | 84 | 33022573 | 1170157 |
| 166 | 85 | 36798433 | 1382953 |
| 168 | 86 | 41478344 | 1628029 |
| 170 | 87 | 46088157 | 1902265 |
| 172 | 88 | 51809031 | 2234133 |
| 174 | 89 | 57417264 | 2601868 |
| 176 | 90 | 64353269 | 3024383 |
| 178 | 91 | 71163452 | 3516365 |
| 180 | 92 | 79538751 | 4071832 |
| 182 | 93 | 87738311 | 4690880 |
| 184 | 94 | 97841183 | 5424777 |
| 186 | 95 | 107679717 | 6229550 |
| 188 | 96 | 119761075 | 7144091 |
| 190 | 97 | 131561744 | 8187581 |
| 192 | 98 | 145976674 | 9364975 |
| 194 | 99 | 159999462 | 10659863 |
| 196 | 100 | 177175687 | 12163298 |
| 198 | 101 | 193814658 | 13809901 |
| 200 | 102 | 214127742 | 15655672 |
| 202 | 103 | 233846463 | 17749388 |
| 204 | 104 | 257815889 | 20070486 |
| 206 | 105 | 281006325 | 22606939 |
| 208 | 106 | 309273526 | 25536557 |
| 210 | 107 | 336500830 | 28700677 |
| 212 | 108 | 369580714 | 32230861 |
| 214 | 109 | 401535955 | 36173081 |
| 216 | 110 | 440216206 | 40536922 |
| 218 | 111 | 477420176 | 45278722 |
| 220 | 112 | 522599564 | 50651799 |
| 222 | 113 | 565900181 | 56463948 |
| 224 | 114 | 618309598 | 62887775 |
| 226 | 115 | 668662698 | 69995887 |
| 228 | 116 | 729414880 | 77831323 |
| 230 | 117 | 787556069 | 86238206 |
| 232 | 118 | 857934016 | 95758929 |
| 234 | 119 | 925042498 | 105965373 |
| 236 | 120 | 1006016526 | 117166528 |
| 238 | 121 | 1083451816 | 129476607 |
| 240 | 122 | 1176632247 | 142960479 |
| 242 | 123 | 1265323971 | 157402781 |
| 244 | 124 | 1372440782 | 173577766 |
| 246 | 125 | 1474111053 | 190809628 |
| 248 | 126 | 1596482232 | 209715141 |
| 250 | 127 | 1712934069 | 230272559 |
| 252 | 128 | 1852762875 | 252745513 |
| 254 | 129 | 1985250572 | 276599787 |
| 256 | 130 | 2144943655 | 303235792 |
| 258 | 131 | 2295793276 | 331516984 |
| 260 | 132 | 2477017558 | 362302637 |
| 262 | 133 | 2648697036 | 395600325 |
| 264 | 134 | 2854536850 | 431894257 |
| 266 | 135 | 3048609900 | 470256444 |
| 268 | 136 | 3282202941 | 512858451 |
| 270 | 137 | 3501931260 | 557745670 |
| 272 | 138 | 3765465341 | 606668511 |
| 274 | 139 | 4014007928 | 659140287 |
| 276 | 140 | 4311652376 | 716217922 |
| 278 | 141 | 4591045471 | 776165188 |
| 280 | 142 | 4926987377 | 842498881 |
| 282 | 143 | 5241548270 | 912274540 |
| 284 | 144 | 5618445787 | 987874095 |
| 286 | 145 | 5972426835 | 1068507788 |
| 288 | 146 | 6395981131 | 1156161307 |
| 290 | 147 | 6791769082 | 1247686189 |
| 292 | 148 | 7267283603 | 1348832364 |
| 294 | 149 | 7710782991 | 1454359806 |
| 296 | 150 | 8241719706 | 1568768524 |
| 298 | 151 | 8738236515 | 1690214836 |
| 300 | 152 | 9332065811 | 1821766896 |
| 302 | 153 | 9884604767 | 1958581588 |
| 304 | 154 | 10548218751 | 2109271290 |
| 306 | 155 | 11164542762 | 2266138871 |
| 308 | 156 | 11902015724 | 2435848971 |
| 310 | 157 | 12588998862 | 2614544391 |
| 312 | 158 | 13410330482 | 2808510141 |
| 314 | 159 | 14171344797 | 3009120113 |
| 316 | 160 | 15085164571 | 3229731630 |
| 318 | 161 | 15930619304 | 3458148016 |
| 320 | 162 | 16942010457 | 3704939275 |
| 322 | 163 | 17880232383 | 3964153268 |
| 324 | 164 | 19002055537 | 4244706701 |
| 326 | 165 | 20037346408 | 4533465777 |
| 328 | 166 | 21280571390 | 4850870260 |
| 330 | 167 | 22426253115 | 5178120469 |
| 332 | 168 | 23796620378 | 5531727283 |
| 334 | 169 | 25063227406 | 5900369830 |
| 336 | 170 | 26577912084 | 6299880577 |
| 338 | 171 | 27970034826 | 6709574675 |
| 340 | 172 | 29642262229 | 7158963073 |
| 342 | 173 | 31177474996 | 7620446934 |
| 344 | 174 | 33014225318 | 8118481242 |
| 346 | 175 | 34705254287 | 8636262789 |
| 348 | 176 | 36728266430 | 9196920285 |
| 350 | 177 | 38580626759 | 9768511147 |
| 352 | 178 | 40806395661 | 10396040696 |
| 354 | 179 | 42842199753 | 11037658075 |
| 356 | 180 | 45278616586 | 11730538496 |
| 358 | 181 | 47513679057 | 12446446419 |
| 360 | 182 | 50189039868 | 13221751502 |
| 362 | 183 | 52628839448 | 14010515381 |
| 364 | 184 | 55562506886 | 14874753568 |
| 366 | 185 | 58236270451 | 15754940959 |
| 368 | 186 | 61437700788 | 16705334454 |
| 370 | 187 | 64363670678 | 17683643273 |
| 372 | 188 | 67868149215 | 18744292915 |
| 374 | 189 | 71052718441 | 19816289281 |
| 376 | 190 | 74884539987 | 20992425825 |
| 378 | 191 | 78364039771 | 22186413139 |
| 380 | 192 | 82532990559 | 23475079272 |
| 382 | 193 | 86329680991 | 24795898388 |
| 384 | 194 | 90881152117 | 26227197453 |
| 386 | 195 | 95001297565 | 27670862550 |
| 388 | 196 | 99963147805 | 29254036711 |
| 390 | 197 | 104453597992 | 30852950986 |
| 392 | 198 | 109837310021 | 32581366295 |
| 394 | 199 | 114722988623 | 34345173894 |
| 396 | 200 | 120585261143 | 36259212641 |
| 398 | 201 | 125873325588 | 38179777473 |
| 400 | 202 | 132247999328 | 40286153024 |
All fullerenes with less than 100 vertices have a spiral starting at a pentagon.
| Vertices | Faces | No pentagon spiral |
|---|---|---|
| 100 | 52 | 1 |
| 102 | 53 | 0 |
| 104 | 54 | 1 |
| 106 | 55 | 0 |
| 108 | 56 | 0 |
| 110 | 57 | 1 |
| 112 | 58 | 0 |
| 114 | 59 | 0 |
| 116 | 60 | 0 |
| 118 | 61 | 0 |
| 120 | 62 | 0 |
| 122 | 63 | 0 |
| 124 | 64 | 1 |
| 126 | 65 | 0 |
| 128 | 66 | 0 |
| 130 | 67 | 0 |
| 132 | 68 | 1 |
| 134 | 69 | 1 |
| 136 | 70 | 1 |
| 138 | 71 | 0 |
| 140 | 72 | 1 |
| 142 | 73 | 0 |
| 144 | 74 | 2 |
| 146 | 75 | 0 |
| 148 | 76 | 2 |
| 150 | 77 | 0 |
| 152 | 78 | 3 |
| 154 | 79 | 0 |
| 156 | 80 | 3 |
| 158 | 81 | 0 |
| 160 | 82 | 1 |
| 162 | 83 | 1 |
| 164 | 84 | 10 |
| 166 | 85 | 3 |
| 168 | 86 | 10 |
| 170 | 87 | 4 |
| 172 | 88 | 8 |
| 174 | 89 | 2 |
| 176 | 90 | 14 |
| 178 | 91 | 6 |
| 180 | 92 | 8 |
| 182 | 93 | 9 |
| 184 | 94 | 16 |
| 186 | 95 | 10 |
| 188 | 96 | 18 |
| 190 | 97 | 6 |
| 192 | 98 | 33 |
| 194 | 99 | 13 |
| 196 | 100 | 34 |
| 198 | 101 | 18 |
| 200 | 102 | 36 |
| 202 | 103 | 25 |
| 204 | 104 | 59 |
| 206 | 105 | 35 |
| 208 | 106 | 66 |
| 210 | 107 | 37 |
| 212 | 108 | 89 |
| 214 | 109 | 57 |
| 216 | 110 | 85 |
| 218 | 111 | 62 |
| 220 | 112 | 87 |
| 222 | 113 | 64 |
| 224 | 114 | 172 |
| 226 | 115 | 99 |
| 228 | 116 | 198 |
| 230 | 117 | 141 |
| 232 | 118 | 194 |
| 234 | 119 | 141 |
| 236 | 120 | 316 |
| 238 | 121 | 205 |
| 240 | 122 | 400 |
| 242 | 123 | 259 |
| 244 | 124 | 468 |
| 246 | 125 | 397 |
| 248 | 126 | 634 |
| 250 | 127 | 411 |
| 252 | 128 | 615 |
| 254 | 129 | 467 |
| 256 | 130 | 851 |
| 258 | 131 | 562 |
| 260 | 132 | 881 |
| 262 | 133 | 623 |
| 264 | 134 | 1083 |
| 266 | 135 | 863 |
| 268 | 136 | 1270 |
| 270 | 137 | 1037 |
| 272 | 138 | 1558 |
| 274 | 139 | 1133 |
| 276 | 140 | 1968 |
| 278 | 141 | 1525 |
| 280 | 142 | 2529 |
| 282 | 143 | 2002 |
| 284 | 144 | 3011 |
| 286 | 145 | 2473 |
| 288 | 146 | 3413 |
| 290 | 147 | 2783 |
| 292 | 148 | 4215 |
| 294 | 149 | 3401 |
| 296 | 150 | 4996 |
| 298 | 151 | 3797 |
| 300 | 152 | 5548 |
| 302 | 153 | 4388 |
| 304 | 154 | 6193 |
| 306 | 155 | 4938 |
| 308 | 156 | 7673 |
| 310 | 157 | 6242 |
| 312 | 158 | 9165 |
| 314 | 159 | 7261 |
| 316 | 160 | 10302 |
| 318 | 161 | 8464 |
| 320 | 162 | 11854 |
| 322 | 163 | 9745 |
| 324 | 164 | 14356 |
| 326 | 165 | 12344 |
| 328 | 166 | 17926 |
| 330 | 167 | 15397 |
| 332 | 168 | 21182 |
| 334 | 169 | 17986 |
| 336 | 170 | 23625 |
| 338 | 171 | 19571 |
| 340 | 172 | 26885 |
| 342 | 173 | 22801 |
| 344 | 174 | 31476 |
| 346 | 175 | 26842 |
| 348 | 176 | 35834 |
| 350 | 177 | 30885 |
| 352 | 178 | 41747 |
| 354 | 179 | 35180 |
| 356 | 180 | 47021 |
| 358 | 181 | 39661 |
| 360 | 182 | 51978 |
| 362 | 183 | 44499 |
| 364 | 184 | 57767 |
| 366 | 185 | 50370 |
| 368 | 186 | 66261 |
| 370 | 187 | 58003 |
| 372 | 188 | 77534 |
| 374 | 189 | 68670 |
| 376 | 190 | 89284 |
| 378 | 191 | 77802 |
| 380 | 192 | 100355 |
| 382 | 193 | 86960 |
| 384 | 194 | 112914 |
| 386 | 195 | 101046 |
| 388 | 196 | 131212 |
| 390 | 197 | 117963 |
| 392 | 198 | 152483 |
| 394 | 199 | 134408 |
| 396 | 200 | 171302 |
| 398 | 201 | 150285 |
| 400 | 202 | 189662 |
| Vertices | Faces | No spiral |
|---|---|---|
| 380 | 192 | 1 |
| 382 | 193 | 0 |
| 384 | 194 | 1 |
| 386 | 195 | 0 |
| 388 | 196 | 0 |
| 390 | 197 | 0 |
| 392 | 198 | 0 |
| 394 | 199 | 0 |
| 396 | 200 | 0 |
| 398 | 201 | 0 |
| 400 | 202 | 0 |
[1] P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Clarendon press, Oxford, 1995.
[2] G. Brinkmann, J. Goedgebeur and B.D. McKay, The smallest fullerene without a spiral, Chemical Physics Letters, 522:54-55, 2012.