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:
The 'face-distance' between two pentagons is the distance between the corresponding vertices of degree 5 in the dual graph. We refer to the least face-distance between pentagons of a fullerene as the 'pentagon separation' of the fullerene. The table below lists the number of fullerenes up to 400 vertices with pentagon separation at least d. Note that d=1 gives the set of all fullerenes and d=2 gives the set of all IPR fullerenes. More information about the pentagon separation of fullerenes can be found in [1].
All fullerene and IPR fullerene counts 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 [2]. More information about spirals in fullerenes can be found in [3].
Vertices | Faces | Fullerenes | IPR Fullerenes | Pent. sep. ≥ 3 | Pent. sep. ≥ 4 | Pent. sep. ≥ 5 |
---|---|---|---|---|---|---|
20 | 12 | 1 | 0 | 0 | 0 | 0 |
22 | 13 | 0 | 0 | 0 | 0 | 0 |
24 | 14 | 1 | 0 | 0 | 0 | 0 |
26 | 15 | 1 | 0 | 0 | 0 | 0 |
28 | 16 | 2 | 0 | 0 | 0 | 0 |
30 | 17 | 3 | 0 | 0 | 0 | 0 |
32 | 18 | 6 | 0 | 0 | 0 | 0 |
34 | 19 | 6 | 0 | 0 | 0 | 0 |
36 | 20 | 15 | 0 | 0 | 0 | 0 |
38 | 21 | 17 | 0 | 0 | 0 | 0 |
40 | 22 | 40 | 0 | 0 | 0 | 0 |
42 | 23 | 45 | 0 | 0 | 0 | 0 |
44 | 24 | 89 | 0 | 0 | 0 | 0 |
46 | 25 | 116 | 0 | 0 | 0 | 0 |
48 | 26 | 199 | 0 | 0 | 0 | 0 |
50 | 27 | 271 | 0 | 0 | 0 | 0 |
52 | 28 | 437 | 0 | 0 | 0 | 0 |
54 | 29 | 580 | 0 | 0 | 0 | 0 |
56 | 30 | 924 | 0 | 0 | 0 | 0 |
58 | 31 | 1205 | 0 | 0 | 0 | 0 |
60 | 32 | 1812 | 1 | 0 | 0 | 0 |
62 | 33 | 2385 | 0 | 0 | 0 | 0 |
64 | 34 | 3465 | 0 | 0 | 0 | 0 |
66 | 35 | 4478 | 0 | 0 | 0 | 0 |
68 | 36 | 6332 | 0 | 0 | 0 | 0 |
70 | 37 | 8149 | 1 | 0 | 0 | 0 |
72 | 38 | 11190 | 1 | 0 | 0 | 0 |
74 | 39 | 14246 | 1 | 0 | 0 | 0 |
76 | 40 | 19151 | 2 | 0 | 0 | 0 |
78 | 41 | 24109 | 5 | 0 | 0 | 0 |
80 | 42 | 31924 | 7 | 0 | 0 | 0 |
82 | 43 | 39718 | 9 | 0 | 0 | 0 |
84 | 44 | 51592 | 24 | 0 | 0 | 0 |
86 | 45 | 63761 | 19 | 0 | 0 | 0 |
88 | 46 | 81738 | 35 | 0 | 0 | 0 |
90 | 47 | 99918 | 46 | 0 | 0 | 0 |
92 | 48 | 126409 | 86 | 0 | 0 | 0 |
94 | 49 | 153493 | 134 | 0 | 0 | 0 |
96 | 50 | 191839 | 187 | 0 | 0 | 0 |
98 | 51 | 231017 | 259 | 0 | 0 | 0 |
100 | 52 | 285914 | 450 | 0 | 0 | 0 |
102 | 53 | 341658 | 616 | 0 | 0 | 0 |
104 | 54 | 419013 | 823 | 0 | 0 | 0 |
106 | 55 | 497529 | 1233 | 0 | 0 | 0 |
108 | 56 | 604217 | 1799 | 0 | 0 | 0 |
110 | 57 | 713319 | 2355 | 0 | 0 | 0 |
112 | 58 | 860161 | 3342 | 0 | 0 | 0 |
114 | 59 | 1008444 | 4468 | 0 | 0 | 0 |
116 | 60 | 1207119 | 6063 | 0 | 0 | 0 |
118 | 61 | 1408553 | 8148 | 0 | 0 | 0 |
120 | 62 | 1674171 | 10774 | 0 | 0 | 0 |
122 | 63 | 1942929 | 13977 | 0 | 0 | 0 |
124 | 64 | 2295721 | 18769 | 0 | 0 | 0 |
126 | 65 | 2650866 | 23589 | 0 | 0 | 0 |
128 | 66 | 3114236 | 30683 | 0 | 0 | 0 |
130 | 67 | 3580637 | 39393 | 0 | 0 | 0 |
132 | 68 | 4182071 | 49878 | 0 | 0 | 0 |
134 | 69 | 4787715 | 62372 | 0 | 0 | 0 |
136 | 70 | 5566949 | 79362 | 0 | 0 | 0 |
138 | 71 | 6344698 | 98541 | 0 | 0 | 0 |
140 | 72 | 7341204 | 121354 | 1 | 0 | 0 |
142 | 73 | 8339033 | 151201 | 0 | 0 | 0 |
144 | 74 | 9604411 | 186611 | 0 | 0 | 0 |
146 | 75 | 10867631 | 225245 | 0 | 0 | 0 |
148 | 76 | 12469092 | 277930 | 0 | 0 | 0 |
150 | 77 | 14059174 | 335569 | 1 | 0 | 0 |
152 | 78 | 16066025 | 404667 | 2 | 0 | 0 |
154 | 79 | 18060979 | 489646 | 0 | 0 | 0 |
156 | 80 | 20558767 | 586264 | 0 | 0 | 0 |
158 | 81 | 23037594 | 697720 | 0 | 0 | 0 |
160 | 82 | 26142839 | 836497 | 2 | 0 | 0 |
162 | 83 | 29202543 | 989495 | 1 | 0 | 0 |
164 | 84 | 33022573 | 1170157 | 2 | 0 | 0 |
166 | 85 | 36798433 | 1382953 | 1 | 0 | 0 |
168 | 86 | 41478344 | 1628029 | 13 | 0 | 0 |
170 | 87 | 46088157 | 1902265 | 4 | 0 | 0 |
172 | 88 | 51809031 | 2234133 | 12 | 0 | 0 |
174 | 89 | 57417264 | 2601868 | 10 | 0 | 0 |
176 | 90 | 64353269 | 3024383 | 28 | 0 | 0 |
178 | 91 | 71163452 | 3516365 | 23 | 0 | 0 |
180 | 92 | 79538751 | 4071832 | 58 | 0 | 0 |
182 | 93 | 87738311 | 4690880 | 54 | 0 | 0 |
184 | 94 | 97841183 | 5424777 | 142 | 0 | 0 |
186 | 95 | 107679717 | 6229550 | 129 | 0 | 0 |
188 | 96 | 119761075 | 7144091 | 291 | 0 | 0 |
190 | 97 | 131561744 | 8187581 | 257 | 0 | 0 |
192 | 98 | 145976674 | 9364975 | 548 | 0 | 0 |
194 | 99 | 159999462 | 10659863 | 566 | 0 | 0 |
196 | 100 | 177175687 | 12163298 | 1126 | 0 | 0 |
198 | 101 | 193814658 | 13809901 | 1072 | 0 | 0 |
200 | 102 | 214127742 | 15655672 | 1943 | 0 | 0 |
202 | 103 | 233846463 | 17749388 | 2080 | 0 | 0 |
204 | 104 | 257815889 | 20070486 | 3682 | 0 | 0 |
206 | 105 | 281006325 | 22606939 | 3992 | 0 | 0 |
208 | 106 | 309273526 | 25536557 | 6340 | 0 | 0 |
210 | 107 | 336500830 | 28700677 | 6737 | 0 | 0 |
212 | 108 | 369580714 | 32230861 | 10513 | 0 | 0 |
214 | 109 | 401535955 | 36173081 | 12000 | 0 | 0 |
216 | 110 | 440216206 | 40536922 | 18169 | 0 | 0 |
218 | 111 | 477420176 | 45278722 | 20019 | 0 | 0 |
220 | 112 | 522599564 | 50651799 | 28528 | 0 | 0 |
222 | 113 | 565900181 | 56463948 | 32276 | 0 | 0 |
224 | 114 | 618309598 | 62887775 | 46534 | 0 | 0 |
226 | 115 | 668662698 | 69995887 | 52177 | 0 | 0 |
228 | 116 | 729414880 | 77831323 | 71303 | 0 | 0 |
230 | 117 | 787556069 | 86238206 | 79915 | 0 | 0 |
232 | 118 | 857934016 | 95758929 | 109848 | 0 | 0 |
234 | 119 | 925042498 | 105965373 | 124153 | 0 | 0 |
236 | 120 | 1006016526 | 117166528 | 164700 | 0 | 0 |
238 | 121 | 1083451816 | 129476607 | 184404 | 0 | 0 |
240 | 122 | 1176632247 | 142960479 | 242507 | 1 | 0 |
242 | 123 | 1265323971 | 157402781 | 273885 | 0 | 0 |
244 | 124 | 1372440782 | 173577766 | 353997 | 0 | 0 |
246 | 125 | 1474111053 | 190809628 | 397673 | 0 | 0 |
248 | 126 | 1596482232 | 209715141 | 507913 | 0 | 0 |
250 | 127 | 1712934069 | 230272559 | 570053 | 0 | 0 |
252 | 128 | 1852762875 | 252745513 | 717983 | 0 | 0 |
254 | 129 | 1985250572 | 276599787 | 805374 | 0 | 0 |
256 | 130 | 2144943655 | 303235792 | 1007680 | 0 | 0 |
258 | 131 | 2295793276 | 331516984 | 1127989 | 0 | 0 |
260 | 132 | 2477017558 | 362302637 | 1392996 | 2 | 0 |
262 | 133 | 2648697036 | 395600325 | 1550580 | 0 | 0 |
264 | 134 | 2854536850 | 431894257 | 1905849 | 0 | 0 |
266 | 135 | 3048609900 | 470256444 | 2124873 | 1 | 0 |
268 | 136 | 3282202941 | 512858451 | 2592104 | 1 | 0 |
270 | 137 | 3501931260 | 557745670 | 2868467 | 2 | 0 |
272 | 138 | 3765465341 | 606668511 | 3461487 | 1 | 0 |
274 | 139 | 4014007928 | 659140287 | 3847594 | 0 | 0 |
276 | 140 | 4311652376 | 716217922 | 4621524 | 1 | 0 |
278 | 141 | 4591045471 | 776165188 | 5112067 | 2 | 0 |
280 | 142 | 4926987377 | 842498881 | 6079570 | 4 | 0 |
282 | 143 | 5241548270 | 912274540 | 6726996 | 1 | 0 |
284 | 144 | 5618445787 | 987874095 | 7971111 | 10 | 0 |
286 | 145 | 5972426835 | 1068507788 | 8784514 | 3 | 0 |
288 | 146 | 6395981131 | 1156161307 | 10352546 | 7 | 0 |
290 | 147 | 6791769082 | 1247686189 | 11385724 | 9 | 0 |
292 | 148 | 7267283603 | 1348832364 | 13357318 | 5 | 0 |
294 | 149 | 7710782991 | 1454359806 | 14652198 | 6 | 0 |
296 | 150 | 8241719706 | 1568768524 | 17102231 | 24 | 0 |
298 | 151 | 8738236515 | 1690214836 | 18756139 | 16 | 0 |
300 | 152 | 9332065811 | 1821766896 | 21766152 | 32 | 0 |
302 | 153 | 9884604767 | 1958581588 | 23815310 | 36 | 0 |
304 | 154 | 10548218751 | 2109271290 | 27529516 | 46 | 0 |
306 | 155 | 11164542762 | 2266138871 | 30090574 | 54 | 0 |
308 | 156 | 11902015724 | 2435848971 | 34629672 | 99 | 0 |
310 | 157 | 12588998862 | 2614544391 | 37770691 | 93 | 0 |
312 | 158 | 13410330482 | 2808510141 | 43312313 | 135 | 0 |
314 | 159 | 14171344797 | 3009120113 | 47153778 | 187 | 0 |
316 | 160 | 15085164571 | 3229731630 | 53899686 | 211 | 0 |
318 | 161 | 15930619304 | 3458148016 | 58585441 | 308 | 0 |
320 | 162 | 16942010457 | 3704939275 | 66712070 | 443 | 0 |
322 | 163 | 17880232383 | 3964153268 | 72395888 | 535 | 0 |
324 | 164 | 19002055537 | 4244706701 | 82171212 | 698 | 0 |
326 | 165 | 20037346408 | 4533465777 | 89063353 | 1026 | 0 |
328 | 166 | 21280571390 | 4850870260 | 100785130 | 1216 | 0 |
330 | 167 | 22426253115 | 5178120469 | 109068073 | 1623 | 0 |
332 | 168 | 23796620378 | 5531727283 | 122992213 | 2489 | 0 |
334 | 169 | 25063227406 | 5900369830 | 132950223 | 2788 | 0 |
336 | 170 | 26577912084 | 6299880577 | 149523121 | 3612 | 0 |
338 | 171 | 27970034826 | 6709574675 | 161430830 | 4744 | 0 |
340 | 172 | 29642262229 | 7158963073 | 181076418 | 5845 | 0 |
342 | 173 | 31177474996 | 7620446934 | 195124334 | 7457 | 0 |
344 | 174 | 33014225318 | 8118481242 | 218323289 | 10591 | 0 |
346 | 175 | 34705254287 | 8636262789 | 235050400 | 12307 | 0 |
348 | 176 | 36728266430 | 9196920285 | 262381050 | 15312 | 0 |
350 | 177 | 38580626759 | 9768511147 | 282042413 | 19574 | 0 |
352 | 178 | 40806395661 | 10396040696 | 314052518 | 23755 | 0 |
354 | 179 | 42842199753 | 11037658075 | 337229970 | 29793 | 0 |
356 | 180 | 45278616586 | 11730538496 | 374666300 | 38688 | 0 |
358 | 181 | 47513679057 | 12446446419 | 401932458 | 45946 | 0 |
360 | 182 | 50189039868 | 13221751502 | 445482235 | 55742 | 0 |
362 | 183 | 52628839448 | 14010515381 | 477264068 | 69970 | 0 |
364 | 184 | 55562506886 | 14874753568 | 528016753 | 83616 | 0 |
366 | 185 | 58236270451 | 15754940959 | 565045586 | 100644 | 0 |
368 | 186 | 61437700788 | 16705334454 | 623895236 | 126048 | 0 |
370 | 187 | 64363670678 | 17683643273 | 666935811 | 149044 | 0 |
372 | 188 | 67868149215 | 18744292915 | 734907336 | 179013 | 0 |
374 | 189 | 71052718441 | 19816289281 | 784797263 | 217673 | 0 |
376 | 190 | 74884539987 | 20992425825 | 863237405 | 257673 | 0 |
378 | 191 | 78364039771 | 22186413139 | 920935351 | 302553 | 0 |
380 | 192 | 82532990559 | 23475079272 | 1011152383 | 367547 | 1 |
382 | 193 | 86329680991 | 24795898388 | 1077679749 | 434339 | 0 |
384 | 194 | 90881152117 | 26227197453 | 1181149036 | 507481 | 0 |
386 | 195 | 95001297565 | 27670862550 | 1257630423 | 611532 | 0 |
388 | 196 | 99963147805 | 29254036711 | 1376400812 | 707184 | 0 |
390 | 197 | 104453597992 | 30852950986 | 1463926563 | 820525 | 0 |
392 | 198 | 109837310021 | 32581366295 | 1599524989 | 982532 | 0 |
394 | 199 | 114722988623 | 34345173894 | 1699970613 | 1133377 | 0 |
396 | 200 | 120585261143 | 36259212641 | 1854374011 | 1323509 | 0 |
398 | 201 | 125873325588 | 38179777473 | 1969147856 | 1546304 | 0 |
400 | 202 | 132247999328 | 40286153024 | 2144985583 | 1784313 | 1 |
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] J. Goedgebeur and B.D. McKay, Fullerenes with distant pentagons, MATCH Commun. Math. Comput. Chem., 74(3):659-672, 2015.
[2] P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Clarendon press, Oxford, 1995.
[3] G. Brinkmann, J. Goedgebeur and B.D. McKay, The smallest fullerene without a spiral, Chemical Physics Letters, 522:54-55, 2012.