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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 column indices minus 2.

Total for a given number of edges:
6	1
7	0
8	1
9	2
10	2
11	4
12	12
13	22
14	58
15	158
16	448
17	1342
18	4199
19	13384
20	43708
21	144810
22	485704
23	1645576
24	5623571
25	19358410
26	67078828
27	233800162
28	819267086
29	2884908430
30	10204782956
31	36249143676
32	129267865144
33	462669746182
34	1661652306539
35	5986979643542