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 |
All fullerenes with less than 380 vertices have a spiral.
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.