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Counting Polyhedra

Using Brendan McKay's published data and plantri software, Stuart E Anderson updated our modest original table. Unlike the rest of the Numericana site, the table on this page is best viewed with a larger screen (1024 pixels or wider). For our general comments, see the original page, which may be viewed at lower resolution (and may also be more suitable for printing).

Vertex Count in row and Face Count in column, or vice-versa
Total (row) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 4 1
2 5 1 1
7 6 1 2 2 2
34 7 2 8 11 8 5
257 8 2 11 42 74 76 38 14
2606 9 8 74 296 633 768 558 219 50
32300 10 5 76 633 2635 6134 8822 7916 4442 1404 233
440564 11 38 768 6134 25626 64439 104213 112082 79773 36528 9714 1249
6384634 12 14 558 8822 64439 268394 709302 1263032 1556952 1338853 789749 306470
96262938 13 219 7916 104213 709302 2937495 8085725 15535572 21395274 21317178 15287112
1496225352 14 50 4442 112082 1263032 8085725 33310550 94713809 193794051 292182191 328192346
23833988129 15 1404 79773 1556952 15535572 94713809 388431688 1134914458 2447709924 3981512855
387591510244 16 233 36528 1338853 21395274 193794051 1134914458 4637550072 13865916560 31277856206
6415851530241 17 9714 789749 21317178 292182191 2447709924 13865916560 56493493990 172301697581
107854282197058 18 1249 306470 15287112 328192346 3981512855 31277856206 172301697581 700335433295
19 70454 7706577 274542869 4939809506 54271705726 404008232288 2173270387051
20 7595 2599554 168992630 4686995652 73247405678 741171341224 5270785332349
21 527235 74424566 3380569040 77220397213 1075323264149 10150757285258
22 49566 22229616 1823658612 63443012728 1240159791730 15683069986564
23 4037671 713331098 40232230880 1136847700529 19547663107721
24 339722 191283058 19322611431 823788552428 19682306885581
25 31477887 6799902944 466224664031 15962912975720
26 2406841 1654924768 201829738768 10348108651919
27 © 2000-2001   Gérard P. Michon  &  Stuart E. Anderson         249026400 64563924319 5288847843415
28 17490241 14386939428 2084335836704
29 1994599707 611239308239
30 129664753 125619037674
31 16147744792
32 977526957
The number of edges is the sum of the row and colums indices minus 2.
Total for a given number of edges:
61
70
81
92
102
114
1212
1322
1458
15158
16448
171342
184199
1913384
2043708
21144810
22485704
231645576
245623571
2519358410
2667078828
27233800162
28819267086
292884908430
3010204782956
3136249143676
32129267865144
33462669746182
341661652306539
355986979643542

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