Polytope of Type {3,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2}*12
if this polytope has a name.
Group : SmallGroup(12,4)
Rank : 3
Schlafli Type : {3,2}
Number of vertices, edges, etc : 3, 3, 2
Order of s0s1s2 : 6
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Projective
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,2} of size 24
{3,2,3} of size 36
{3,2,4} of size 48
{3,2,5} of size 60
{3,2,6} of size 72
{3,2,7} of size 84
{3,2,8} of size 96
{3,2,9} of size 108
{3,2,10} of size 120
{3,2,11} of size 132
{3,2,12} of size 144
{3,2,13} of size 156
{3,2,14} of size 168
{3,2,15} of size 180
{3,2,16} of size 192
{3,2,17} of size 204
{3,2,18} of size 216
{3,2,19} of size 228
{3,2,20} of size 240
{3,2,21} of size 252
{3,2,22} of size 264
{3,2,23} of size 276
{3,2,24} of size 288
{3,2,25} of size 300
{3,2,26} of size 312
{3,2,27} of size 324
{3,2,28} of size 336
{3,2,29} of size 348
{3,2,30} of size 360
{3,2,31} of size 372
{3,2,32} of size 384
{3,2,33} of size 396
{3,2,34} of size 408
{3,2,35} of size 420
{3,2,36} of size 432
{3,2,37} of size 444
{3,2,38} of size 456
{3,2,39} of size 468
{3,2,40} of size 480
{3,2,41} of size 492
{3,2,42} of size 504
{3,2,43} of size 516
{3,2,44} of size 528
{3,2,45} of size 540
{3,2,46} of size 552
{3,2,47} of size 564
{3,2,48} of size 576
{3,2,49} of size 588
{3,2,50} of size 600
{3,2,51} of size 612
{3,2,52} of size 624
{3,2,53} of size 636
{3,2,54} of size 648
{3,2,55} of size 660
{3,2,56} of size 672
{3,2,57} of size 684
{3,2,58} of size 696
{3,2,59} of size 708
{3,2,60} of size 720
{3,2,61} of size 732
{3,2,62} of size 744
{3,2,63} of size 756
{3,2,64} of size 768
{3,2,65} of size 780
{3,2,66} of size 792
{3,2,67} of size 804
{3,2,68} of size 816
{3,2,69} of size 828
{3,2,70} of size 840
{3,2,71} of size 852
{3,2,72} of size 864
{3,2,73} of size 876
{3,2,74} of size 888
{3,2,75} of size 900
{3,2,76} of size 912
{3,2,77} of size 924
{3,2,78} of size 936
{3,2,79} of size 948
{3,2,80} of size 960
{3,2,81} of size 972
{3,2,82} of size 984
{3,2,83} of size 996
{3,2,84} of size 1008
{3,2,85} of size 1020
{3,2,86} of size 1032
{3,2,87} of size 1044
{3,2,88} of size 1056
{3,2,89} of size 1068
{3,2,90} of size 1080
{3,2,91} of size 1092
{3,2,92} of size 1104
{3,2,93} of size 1116
{3,2,94} of size 1128
{3,2,95} of size 1140
{3,2,96} of size 1152
{3,2,97} of size 1164
{3,2,98} of size 1176
{3,2,99} of size 1188
{3,2,100} of size 1200
{3,2,101} of size 1212
{3,2,102} of size 1224
{3,2,103} of size 1236
{3,2,104} of size 1248
{3,2,105} of size 1260
{3,2,106} of size 1272
{3,2,107} of size 1284
{3,2,108} of size 1296
{3,2,109} of size 1308
{3,2,110} of size 1320
{3,2,111} of size 1332
{3,2,112} of size 1344
{3,2,113} of size 1356
{3,2,114} of size 1368
{3,2,115} of size 1380
{3,2,116} of size 1392
{3,2,117} of size 1404
{3,2,118} of size 1416
{3,2,119} of size 1428
{3,2,120} of size 1440
{3,2,121} of size 1452
{3,2,122} of size 1464
{3,2,123} of size 1476
{3,2,124} of size 1488
{3,2,125} of size 1500
{3,2,126} of size 1512
{3,2,127} of size 1524
{3,2,129} of size 1548
{3,2,130} of size 1560
{3,2,131} of size 1572
{3,2,132} of size 1584
{3,2,133} of size 1596
{3,2,134} of size 1608
{3,2,135} of size 1620
{3,2,136} of size 1632
{3,2,137} of size 1644
{3,2,138} of size 1656
{3,2,139} of size 1668
{3,2,140} of size 1680
{3,2,141} of size 1692
{3,2,142} of size 1704
{3,2,143} of size 1716
{3,2,144} of size 1728
{3,2,145} of size 1740
{3,2,146} of size 1752
{3,2,147} of size 1764
{3,2,148} of size 1776
{3,2,149} of size 1788
{3,2,150} of size 1800
{3,2,151} of size 1812
{3,2,152} of size 1824
{3,2,153} of size 1836
{3,2,154} of size 1848
{3,2,155} of size 1860
{3,2,156} of size 1872
{3,2,157} of size 1884
{3,2,158} of size 1896
{3,2,159} of size 1908
{3,2,160} of size 1920
{3,2,161} of size 1932
{3,2,162} of size 1944
{3,2,163} of size 1956
{3,2,164} of size 1968
{3,2,165} of size 1980
{3,2,166} of size 1992
Vertex Figure Of :
{2,3,2} of size 24
{3,3,2} of size 48
{4,3,2} of size 48
{6,3,2} of size 72
{4,3,2} of size 96
{6,3,2} of size 96
{5,3,2} of size 120
{8,3,2} of size 192
{12,3,2} of size 192
{6,3,2} of size 216
{5,3,2} of size 240
{10,3,2} of size 240
{10,3,2} of size 240
{6,3,2} of size 288
{12,3,2} of size 288
{6,3,2} of size 384
{8,3,2} of size 384
{10,3,2} of size 480
{12,3,2} of size 576
{24,3,2} of size 576
{6,3,2} of size 600
{10,3,2} of size 600
{6,3,2} of size 648
{18,3,2} of size 648
{7,3,2} of size 672
{8,3,2} of size 672
{8,3,2} of size 672
{10,3,2} of size 720
{15,3,2} of size 720
{8,3,2} of size 768
{12,3,2} of size 768
{6,3,2} of size 864
{12,3,2} of size 864
{20,3,2} of size 960
{7,3,2} of size 1008
{9,3,2} of size 1008
{6,3,2} of size 1152
{24,3,2} of size 1152
{12,3,2} of size 1152
{6,3,2} of size 1176
{14,3,2} of size 1176
{9,3,2} of size 1296
{12,3,2} of size 1296
{8,3,2} of size 1344
{8,3,2} of size 1344
{14,3,2} of size 1344
{8,3,2} of size 1440
{10,3,2} of size 1440
{10,3,2} of size 1440
{30,3,2} of size 1440
{12,3,2} of size 1728
{24,3,2} of size 1728
{6,3,2} of size 1800
{30,3,2} of size 1800
{18,3,2} of size 1944
{6,3,2} of size 1944
{18,3,2} of size 1944
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,2}*24
3-fold covers : {9,2}*36, {3,6}*36
4-fold covers : {12,2}*48, {6,4}*48a, {3,4}*48
5-fold covers : {15,2}*60
6-fold covers : {18,2}*72, {6,6}*72a, {6,6}*72c
7-fold covers : {21,2}*84
8-fold covers : {12,4}*96a, {24,2}*96, {6,8}*96, {3,8}*96, {6,4}*96
9-fold covers : {27,2}*108, {9,6}*108, {3,6}*108
10-fold covers : {6,10}*120, {30,2}*120
11-fold covers : {33,2}*132
12-fold covers : {36,2}*144, {18,4}*144a, {9,4}*144, {6,12}*144a, {12,6}*144a, {12,6}*144b, {6,12}*144c, {3,6}*144, {3,12}*144
13-fold covers : {39,2}*156
14-fold covers : {6,14}*168, {42,2}*168
15-fold covers : {45,2}*180, {15,6}*180
16-fold covers : {24,4}*192a, {12,4}*192a, {24,4}*192b, {12,8}*192a, {12,8}*192b, {48,2}*192, {6,16}*192, {3,8}*192, {12,4}*192b, {6,4}*192b, {12,4}*192c, {6,8}*192b, {6,8}*192c
17-fold covers : {51,2}*204
18-fold covers : {54,2}*216, {6,18}*216a, {18,6}*216a, {18,6}*216b, {6,6}*216b, {6,6}*216c, {6,6}*216d
19-fold covers : {57,2}*228
20-fold covers : {12,10}*240, {6,20}*240a, {60,2}*240, {30,4}*240a, {15,4}*240
21-fold covers : {63,2}*252, {21,6}*252
22-fold covers : {6,22}*264, {66,2}*264
23-fold covers : {69,2}*276
24-fold covers : {36,4}*288a, {72,2}*288, {18,8}*288, {9,8}*288, {6,24}*288a, {24,6}*288a, {24,6}*288b, {12,12}*288a, {12,12}*288c, {6,24}*288c, {18,4}*288, {3,12}*288, {3,24}*288, {6,6}*288b, {6,12}*288a, {6,12}*288b, {12,6}*288a
25-fold covers : {75,2}*300, {3,10}*300, {15,10}*300
26-fold covers : {6,26}*312, {78,2}*312
27-fold covers : {81,2}*324, {9,18}*324, {9,6}*324a, {27,6}*324, {9,6}*324b, {9,6}*324c, {9,6}*324d, {3,6}*324, {3,18}*324
28-fold covers : {12,14}*336, {6,28}*336a, {84,2}*336, {42,4}*336a, {21,4}*336
29-fold covers : {87,2}*348
30-fold covers : {18,10}*360, {90,2}*360, {6,30}*360a, {6,30}*360b, {30,6}*360b, {30,6}*360c
31-fold covers : {93,2}*372
32-fold covers : {24,4}*384a, {24,8}*384a, {24,8}*384b, {12,8}*384a, {24,8}*384c, {24,8}*384d, {48,4}*384a, {48,4}*384b, {12,4}*384a, {24,4}*384b, {12,8}*384b, {12,16}*384a, {12,16}*384b, {96,2}*384, {6,32}*384, {3,8}*384, {6,8}*384a, {12,4}*384d, {12,8}*384e, {12,8}*384f, {6,4}*384a, {6,8}*384d, {6,8}*384e, {6,8}*384f, {12,8}*384g, {12,8}*384h, {24,4}*384c, {24,4}*384d, {6,8}*384g, {12,4}*384e, {24,4}*384e, {6,4}*384b, {24,4}*384f
33-fold covers : {99,2}*396, {33,6}*396
34-fold covers : {6,34}*408, {102,2}*408
35-fold covers : {105,2}*420
36-fold covers : {108,2}*432, {54,4}*432a, {27,4}*432, {6,36}*432a, {36,6}*432a, {36,6}*432b, {12,18}*432a, {18,12}*432a, {6,12}*432b, {12,6}*432a, {12,6}*432b, {18,12}*432b, {6,12}*432c, {9,6}*432, {9,12}*432, {3,6}*432, {3,12}*432, {6,12}*432g, {12,6}*432g, {6,4}*432b, {12,4}*432b, {12,6}*432i
37-fold covers : {111,2}*444
38-fold covers : {6,38}*456, {114,2}*456
39-fold covers : {117,2}*468, {39,6}*468
40-fold covers : {24,10}*480, {6,40}*480, {12,20}*480, {60,4}*480a, {120,2}*480, {30,8}*480, {15,8}*480, {6,20}*480c, {30,4}*480
41-fold covers : {123,2}*492
42-fold covers : {18,14}*504, {126,2}*504, {6,42}*504a, {6,42}*504b, {42,6}*504b, {42,6}*504c
43-fold covers : {129,2}*516
44-fold covers : {12,22}*528, {6,44}*528a, {132,2}*528, {66,4}*528a, {33,4}*528
45-fold covers : {135,2}*540, {45,6}*540, {15,6}*540
46-fold covers : {6,46}*552, {138,2}*552
47-fold covers : {141,2}*564
48-fold covers : {72,4}*576a, {36,4}*576a, {72,4}*576b, {36,8}*576a, {36,8}*576b, {144,2}*576, {18,16}*576, {9,8}*576, {6,48}*576a, {48,6}*576a, {48,6}*576b, {12,24}*576a, {12,12}*576a, {12,12}*576c, {12,24}*576b, {12,24}*576c, {24,12}*576c, {24,12}*576d, {12,24}*576e, {24,12}*576e, {24,12}*576f, {6,48}*576c, {36,4}*576b, {18,4}*576b, {36,4}*576c, {18,8}*576b, {18,8}*576c, {3,6}*576, {3,24}*576, {12,12}*576d, {12,12}*576e, {12,12}*576f, {6,12}*576b, {12,6}*576a, {12,6}*576b, {12,12}*576h, {6,12}*576c, {6,24}*576b, {6,6}*576b, {6,24}*576c, {6,24}*576d, {24,6}*576c, {6,24}*576e, {12,6}*576d, {24,6}*576e, {6,12}*576e, {6,12}*576f, {12,12}*576j, {12,12}*576k, {3,12}*576, {6,6}*576e
49-fold covers : {147,2}*588, {3,14}*588, {21,14}*588
50-fold covers : {6,50}*600, {150,2}*600, {6,10}*600a, {6,10}*600b, {30,10}*600a, {30,10}*600b, {30,10}*600c
51-fold covers : {153,2}*612, {51,6}*612
52-fold covers : {12,26}*624, {6,52}*624a, {156,2}*624, {78,4}*624a, {39,4}*624
53-fold covers : {159,2}*636
54-fold covers : {162,2}*648, {18,18}*648a, {18,18}*648c, {6,18}*648b, {18,6}*648a, {18,6}*648b, {6,54}*648a, {54,6}*648a, {54,6}*648b, {6,6}*648a, {6,6}*648b, {18,6}*648c, {18,6}*648d, {6,18}*648f, {18,6}*648e, {18,6}*648f, {6,6}*648d, {6,18}*648g, {6,18}*648h, {18,6}*648g, {6,18}*648i, {18,6}*648i, {6,6}*648e, {6,6}*648f, {6,6}*648g
55-fold covers : {165,2}*660
56-fold covers : {24,14}*672, {6,56}*672, {12,28}*672, {84,4}*672a, {168,2}*672, {42,8}*672, {21,8}*672, {6,28}*672, {42,4}*672
57-fold covers : {171,2}*684, {57,6}*684
58-fold covers : {6,58}*696, {174,2}*696
59-fold covers : {177,2}*708
60-fold covers : {36,10}*720, {18,20}*720a, {180,2}*720, {90,4}*720a, {45,4}*720, {6,60}*720a, {12,30}*720a, {12,30}*720b, {30,12}*720b, {6,60}*720b, {60,6}*720b, {60,6}*720c, {30,12}*720c, {15,4}*720, {15,6}*720a, {3,10}*720b, {15,6}*720c, {15,10}*720, {15,12}*720, {15,6}*720e
61-fold covers : {183,2}*732
62-fold covers : {6,62}*744, {186,2}*744
63-fold covers : {189,2}*756, {63,6}*756, {21,6}*756
64-fold covers : {24,8}*768a, {12,8}*768a, {24,8}*768b, {24,4}*768a, {24,8}*768c, {24,8}*768d, {12,16}*768a, {48,4}*768a, {12,16}*768b, {48,4}*768b, {48,8}*768a, {24,16}*768a, {48,8}*768b, {24,16}*768b, {24,16}*768c, {48,8}*768c, {48,8}*768d, {24,16}*768d, {24,16}*768e, {48,8}*768e, {48,8}*768f, {24,16}*768f, {12,32}*768a, {96,4}*768a, {12,32}*768b, {96,4}*768b, {12,4}*768a, {24,4}*768b, {12,8}*768b, {12,8}*768c, {24,8}*768e, {24,4}*768c, {24,4}*768d, {12,8}*768d, {24,8}*768f, {24,8}*768g, {24,8}*768h, {6,64}*768, {192,2}*768, {3,16}*768a, {3,16}*768b, {6,8}*768d, {12,8}*768k, {6,8}*768e, {6,8}*768f, {12,8}*768l, {6,8}*768g, {6,8}*768h, {6,8}*768i, {12,8}*768m, {12,8}*768n, {24,8}*768i, {24,8}*768j, {24,8}*768k, {24,8}*768l, {6,8}*768j, {24,8}*768m, {12,8}*768o, {24,8}*768n, {12,8}*768p, {24,8}*768o, {24,8}*768p, {12,4}*768b, {6,4}*768a, {12,4}*768c, {12,8}*768q, {12,8}*768r, {12,8}*768s, {24,4}*768i, {12,4}*768d, {12,8}*768t, {24,4}*768j, {12,8}*768u, {12,4}*768e, {24,4}*768k, {6,8}*768k, {12,8}*768v, {12,8}*768w, {12,4}*768f, {24,4}*768l, {6,8}*768l, {12,8}*768x, {6,8}*768m, {6,8}*768n, {6,4}*768b, {6,4}*768c, {12,4}*768g, {12,4}*768h, {48,4}*768c, {48,4}*768d, {6,16}*768b, {6,16}*768c
65-fold covers : {195,2}*780
66-fold covers : {18,22}*792, {198,2}*792, {6,66}*792a, {6,66}*792b, {66,6}*792b, {66,6}*792c
67-fold covers : {201,2}*804
68-fold covers : {12,34}*816, {6,68}*816a, {204,2}*816, {102,4}*816a, {51,4}*816
69-fold covers : {207,2}*828, {69,6}*828
70-fold covers : {30,14}*840, {42,10}*840, {6,70}*840, {210,2}*840
71-fold covers : {213,2}*852
72-fold covers : {108,4}*864a, {216,2}*864, {54,8}*864, {27,8}*864, {6,72}*864a, {72,6}*864a, {72,6}*864b, {18,24}*864a, {24,18}*864a, {6,24}*864b, {24,6}*864a, {24,6}*864b, {12,36}*864a, {36,12}*864a, {36,12}*864b, {12,12}*864a, {12,12}*864c, {18,24}*864b, {6,24}*864c, {54,4}*864, {9,12}*864, {9,24}*864, {3,12}*864, {3,24}*864, {6,24}*864f, {24,6}*864f, {12,12}*864h, {6,36}*864, {18,6}*864, {36,6}*864, {12,18}*864a, {18,12}*864a, {18,12}*864b, {6,6}*864a, {6,12}*864a, {6,12}*864b, {12,6}*864b, {12,4}*864c, {12,4}*864d, {6,8}*864b, {24,6}*864h, {12,12}*864k, {6,6}*864c, {6,12}*864c, {12,6}*864c
73-fold covers : {219,2}*876
74-fold covers : {6,74}*888, {222,2}*888
75-fold covers : {225,2}*900, {75,6}*900, {9,10}*900, {45,10}*900, {3,6}*900, {3,30}*900, {15,30}*900
76-fold covers : {12,38}*912, {6,76}*912a, {228,2}*912, {114,4}*912a, {57,4}*912
77-fold covers : {231,2}*924
78-fold covers : {18,26}*936, {234,2}*936, {6,78}*936a, {6,78}*936b, {78,6}*936b, {78,6}*936c
79-fold covers : {237,2}*948
80-fold covers : {48,10}*960, {6,80}*960, {12,20}*960a, {24,20}*960a, {12,40}*960a, {24,20}*960b, {12,40}*960b, {120,4}*960a, {60,4}*960a, {120,4}*960b, {60,8}*960a, {60,8}*960b, {240,2}*960, {30,16}*960, {15,8}*960a, {12,20}*960b, {6,20}*960e, {6,40}*960d, {6,40}*960e, {12,20}*960c, {60,4}*960b, {30,4}*960b, {60,4}*960c, {30,8}*960b, {30,8}*960c, {15,10}*960, {15,4}*960
81-fold covers : {243,2}*972, {9,18}*972a, {3,18}*972a, {9,6}*972a, {9,6}*972b, {9,18}*972b, {9,6}*972c, {9,18}*972c, {9,18}*972d, {9,18}*972e, {27,18}*972, {27,6}*972a, {9,6}*972d, {9,18}*972f, {9,18}*972g, {9,18}*972h, {9,18}*972i, {9,6}*972e, {9,18}*972j, {27,6}*972b, {27,6}*972c, {81,6}*972, {3,6}*972, {3,18}*972b
82-fold covers : {6,82}*984, {246,2}*984
83-fold covers : {249,2}*996
84-fold covers : {36,14}*1008, {18,28}*1008a, {252,2}*1008, {126,4}*1008a, {63,4}*1008, {6,84}*1008a, {12,42}*1008a, {12,42}*1008b, {42,12}*1008b, {6,84}*1008b, {84,6}*1008b, {84,6}*1008c, {42,12}*1008c, {21,12}*1008, {21,6}*1008b
85-fold covers : {255,2}*1020
86-fold covers : {6,86}*1032, {258,2}*1032
87-fold covers : {261,2}*1044, {87,6}*1044
88-fold covers : {24,22}*1056, {6,88}*1056, {12,44}*1056, {132,4}*1056a, {264,2}*1056, {66,8}*1056, {33,8}*1056, {6,44}*1056, {66,4}*1056
89-fold covers : {267,2}*1068
90-fold covers : {54,10}*1080, {270,2}*1080, {18,30}*1080a, {6,30}*1080a, {6,90}*1080a, {90,6}*1080a, {90,6}*1080b, {18,30}*1080b, {30,18}*1080b, {6,30}*1080c, {30,6}*1080b, {30,6}*1080c, {6,30}*1080d, {30,6}*1080d
91-fold covers : {273,2}*1092
92-fold covers : {12,46}*1104, {6,92}*1104a, {276,2}*1104, {138,4}*1104a, {69,4}*1104
93-fold covers : {279,2}*1116, {93,6}*1116
94-fold covers : {6,94}*1128, {282,2}*1128
95-fold covers : {285,2}*1140
96-fold covers : {36,8}*1152a, {72,4}*1152a, {12,24}*1152b, {24,12}*1152a, {24,12}*1152b, {12,24}*1152c, {72,8}*1152a, {72,8}*1152b, {72,8}*1152c, {24,24}*1152b, {24,24}*1152c, {24,24}*1152d, {24,24}*1152e, {24,24}*1152g, {24,24}*1152i, {72,8}*1152d, {24,24}*1152k, {24,24}*1152l, {36,16}*1152a, {144,4}*1152a, {12,48}*1152b, {48,12}*1152a, {48,12}*1152b, {12,48}*1152c, {36,16}*1152b, {144,4}*1152b, {12,48}*1152e, {48,12}*1152d, {48,12}*1152e, {12,48}*1152f, {36,4}*1152a, {72,4}*1152b, {36,8}*1152b, {12,12}*1152a, {12,24}*1152d, {12,24}*1152e, {24,12}*1152e, {12,12}*1152c, {24,12}*1152f, {18,32}*1152, {288,2}*1152, {6,96}*1152a, {6,96}*1152c, {96,6}*1152b, {96,6}*1152c, {9,8}*1152, {18,8}*1152a, {36,4}*1152d, {36,8}*1152e, {36,8}*1152f, {18,4}*1152a, {18,8}*1152d, {18,8}*1152e, {18,8}*1152f, {36,8}*1152g, {36,8}*1152h, {72,4}*1152c, {72,4}*1152d, {18,8}*1152g, {36,4}*1152e, {72,4}*1152e, {18,4}*1152b, {72,4}*1152f, {3,12}*1152a, {3,24}*1152a, {6,24}*1152a, {6,6}*1152a, {6,24}*1152b, {6,24}*1152c, {24,6}*1152b, {12,24}*1152i, {12,24}*1152j, {24,12}*1152i, {12,12}*1152e, {12,24}*1152k, {12,24}*1152l, {24,12}*1152k, {12,12}*1152g, {12,24}*1152m, {6,24}*1152d, {12,6}*1152a, {12,24}*1152n, {24,6}*1152d, {6,6}*1152d, {6,12}*1152b, {6,12}*1152c, {12,6}*1152b, {6,6}*1152f, {6,24}*1152e, {6,24}*1152f, {24,6}*1152e, {12,24}*1152o, {24,12}*1152o, {24,12}*1152p, {12,24}*1152q, {24,12}*1152q, {24,12}*1152r, {6,24}*1152h, {24,6}*1152g, {24,6}*1152h, {6,12}*1152d, {12,6}*1152d, {24,6}*1152i, {24,12}*1152s, {12,12}*1152h, {12,12}*1152i, {24,12}*1152t, {12,12}*1152k, {12,12}*1152l, {12,12}*1152m, {12,12}*1152n, {6,24}*1152j, {6,24}*1152k, {6,12}*1152e, {6,24}*1152l, {12,24}*1152u, {24,12}*1152u, {12,12}*1152q, {12,24}*1152v, {24,12}*1152v, {12,12}*1152s, {12,24}*1152w, {24,12}*1152w, {6,12}*1152f, {6,24}*1152m, {12,24}*1152x, {24,12}*1152x, {3,12}*1152b, {3,24}*1152b, {6,12}*1152g, {3,24}*1152c, {12,6}*1152h, {12,6}*1152i, {6,12}*1152j, {12,12}*1152t, {6,6}*1152i, {6,6}*1152j
97-fold covers : {291,2}*1164
98-fold covers : {6,98}*1176, {294,2}*1176, {6,14}*1176a, {6,14}*1176b, {42,14}*1176a, {42,14}*1176b, {42,14}*1176c
99-fold covers : {297,2}*1188, {99,6}*1188, {33,6}*1188
100-fold covers : {12,50}*1200, {6,100}*1200a, {300,2}*1200, {150,4}*1200a, {75,4}*1200, {6,20}*1200a, {12,10}*1200a, {12,10}*1200b, {6,20}*1200b, {30,20}*1200a, {60,10}*1200a, {30,20}*1200b, {60,10}*1200b, {60,10}*1200c, {30,20}*1200c, {12,4}*1200, {30,4}*1200b, {15,20}*1200, {3,20}*1200, {12,10}*1200c
101-fold covers : {303,2}*1212
102-fold covers : {18,34}*1224, {306,2}*1224, {6,102}*1224a, {6,102}*1224b, {102,6}*1224b, {102,6}*1224c
103-fold covers : {309,2}*1236
104-fold covers : {24,26}*1248, {6,104}*1248, {12,52}*1248, {156,4}*1248a, {312,2}*1248, {78,8}*1248, {39,8}*1248, {6,52}*1248, {78,4}*1248
105-fold covers : {315,2}*1260, {105,6}*1260
106-fold covers : {6,106}*1272, {318,2}*1272
107-fold covers : {321,2}*1284
108-fold covers : {324,2}*1296, {162,4}*1296a, {81,4}*1296, {18,36}*1296a, {36,18}*1296a, {36,18}*1296b, {12,18}*1296a, {18,12}*1296a, {6,36}*1296b, {36,6}*1296a, {36,6}*1296b, {12,54}*1296a, {54,12}*1296a, {6,108}*1296a, {108,6}*1296a, {108,6}*1296b, {6,12}*1296a, {12,6}*1296a, {36,6}*1296c, {6,12}*1296b, {12,6}*1296b, {36,6}*1296d, {12,18}*1296b, {18,12}*1296b, {6,36}*1296f, {36,6}*1296e, {36,6}*1296f, {12,18}*1296c, {12,18}*1296d, {18,12}*1296c, {6,36}*1296g, {12,6}*1296c, {36,6}*1296g, {18,36}*1296c, {18,12}*1296e, {54,12}*1296b, {18,12}*1296f, {18,12}*1296g, {18,12}*1296h, {6,12}*1296d, {6,36}*1296h, {27,6}*1296, {27,12}*1296, {9,18}*1296a, {9,36}*1296, {9,6}*1296a, {3,6}*1296, {3,36}*1296, {9,6}*1296b, {3,12}*1296a, {3,18}*1296a, {9,12}*1296a, {9,6}*1296c, {9,12}*1296b, {9,12}*1296c, {9,6}*1296d, {9,12}*1296d, {6,36}*1296l, {36,6}*1296l, {12,18}*1296l, {18,12}*1296l, {6,12}*1296g, {6,12}*1296h, {12,6}*1296g, {12,6}*1296h, {6,12}*1296i, {12,6}*1296i, {18,4}*1296b, {36,4}*1296, {6,4}*1296a, {6,12}*1296j, {6,12}*1296l, {12,4}*1296, {12,12}*1296c, {12,12}*1296d, {36,6}*1296m, {12,6}*1296o, {36,6}*1296n, {36,6}*1296o, {9,4}*1296a, {3,12}*1296b, {9,4}*1296b, {9,12}*1296e, {9,12}*1296f, {6,12}*1296s, {12,12}*1296f, {6,12}*1296t, {12,6}*1296t, {12,6}*1296u, {12,12}*1296h
109-fold covers : {327,2}*1308
110-fold covers : {30,22}*1320, {66,10}*1320, {6,110}*1320, {330,2}*1320
111-fold covers : {333,2}*1332, {111,6}*1332
112-fold covers : {48,14}*1344, {6,112}*1344, {12,28}*1344a, {24,28}*1344a, {12,56}*1344a, {24,28}*1344b, {12,56}*1344b, {168,4}*1344a, {84,4}*1344a, {168,4}*1344b, {84,8}*1344a, {84,8}*1344b, {336,2}*1344, {42,16}*1344, {21,8}*1344, {12,28}*1344b, {6,28}*1344e, {6,56}*1344b, {6,56}*1344c, {12,28}*1344c, {84,4}*1344b, {42,4}*1344b, {84,4}*1344c, {42,8}*1344b, {42,8}*1344c
113-fold covers : {339,2}*1356
114-fold covers : {18,38}*1368, {342,2}*1368, {6,114}*1368a, {6,114}*1368b, {114,6}*1368b, {114,6}*1368c
115-fold covers : {345,2}*1380
116-fold covers : {12,58}*1392, {6,116}*1392a, {348,2}*1392, {174,4}*1392a, {87,4}*1392
117-fold covers : {351,2}*1404, {117,6}*1404, {39,6}*1404
118-fold covers : {6,118}*1416, {354,2}*1416
119-fold covers : {357,2}*1428
120-fold covers : {72,10}*1440, {18,40}*1440, {36,20}*1440, {180,4}*1440a, {360,2}*1440, {90,8}*1440, {45,8}*1440, {6,120}*1440a, {24,30}*1440a, {12,60}*1440a, {24,30}*1440b, {30,24}*1440b, {6,120}*1440b, {120,6}*1440b, {120,6}*1440c, {12,60}*1440b, {60,12}*1440b, {60,12}*1440c, {30,24}*1440c, {18,20}*1440, {90,4}*1440, {15,6}*1440b, {15,8}*1440, {30,6}*1440b, {3,20}*1440a, {15,12}*1440b, {15,20}*1440a, {15,24}*1440, {15,12}*1440c, {6,4}*1440b, {6,6}*1440d, {6,10}*1440e, {12,6}*1440c, {12,10}*1440g, {30,4}*1440, {30,6}*1440c, {6,10}*1440f, {30,6}*1440e, {30,10}*1440, {6,30}*1440g, {6,60}*1440c, {12,30}*1440a, {30,12}*1440a, {30,12}*1440b, {6,60}*1440d, {30,6}*1440h, {60,6}*1440d
121-fold covers : {363,2}*1452, {3,22}*1452, {33,22}*1452
122-fold covers : {6,122}*1464, {366,2}*1464
123-fold covers : {369,2}*1476, {123,6}*1476
124-fold covers : {12,62}*1488, {6,124}*1488a, {372,2}*1488, {186,4}*1488a, {93,4}*1488
125-fold covers : {375,2}*1500, {3,10}*1500, {15,10}*1500a, {15,10}*1500b, {15,10}*1500c, {15,10}*1500d, {75,10}*1500, {15,10}*1500e, {15,10}*1500f, {15,10}*1500g
126-fold covers : {54,14}*1512, {378,2}*1512, {18,42}*1512a, {6,42}*1512a, {6,126}*1512a, {126,6}*1512a, {126,6}*1512b, {18,42}*1512b, {42,18}*1512b, {6,42}*1512c, {42,6}*1512b, {42,6}*1512c, {6,42}*1512d, {42,6}*1512d
127-fold covers : {381,2}*1524
129-fold covers : {387,2}*1548, {129,6}*1548
130-fold covers : {30,26}*1560, {78,10}*1560, {6,130}*1560, {390,2}*1560
131-fold covers : {393,2}*1572
132-fold covers : {36,22}*1584, {18,44}*1584a, {396,2}*1584, {198,4}*1584a, {99,4}*1584, {6,132}*1584a, {12,66}*1584a, {12,66}*1584b, {66,12}*1584b, {6,132}*1584b, {132,6}*1584b, {132,6}*1584c, {66,12}*1584c, {33,12}*1584, {33,6}*1584
133-fold covers : {399,2}*1596
134-fold covers : {6,134}*1608, {402,2}*1608
135-fold covers : {405,2}*1620, {45,18}*1620, {45,6}*1620a, {135,6}*1620, {45,6}*1620b, {45,6}*1620c, {45,6}*1620d, {15,6}*1620, {15,18}*1620
136-fold covers : {24,34}*1632, {6,136}*1632, {12,68}*1632, {204,4}*1632a, {408,2}*1632, {102,8}*1632, {51,8}*1632, {6,68}*1632, {102,4}*1632
137-fold covers : {411,2}*1644
138-fold covers : {18,46}*1656, {414,2}*1656, {6,138}*1656a, {6,138}*1656b, {138,6}*1656b, {138,6}*1656c
139-fold covers : {417,2}*1668
140-fold covers : {60,14}*1680, {30,28}*1680a, {42,20}*1680a, {84,10}*1680, {12,70}*1680, {6,140}*1680a, {420,2}*1680, {210,4}*1680a, {105,4}*1680
141-fold covers : {423,2}*1692, {141,6}*1692
142-fold covers : {6,142}*1704, {426,2}*1704
143-fold covers : {429,2}*1716
144-fold covers : {216,4}*1728a, {108,4}*1728a, {216,4}*1728b, {108,8}*1728a, {108,8}*1728b, {432,2}*1728, {54,16}*1728, {27,8}*1728, {6,144}*1728a, {144,6}*1728a, {144,6}*1728b, {18,48}*1728a, {48,18}*1728a, {6,48}*1728b, {48,6}*1728a, {48,6}*1728b, {36,24}*1728a, {12,24}*1728a, {12,36}*1728a, {36,12}*1728a, {36,12}*1728b, {12,12}*1728a, {12,12}*1728c, {36,24}*1728b, {12,24}*1728b, {12,72}*1728a, {72,12}*1728a, {72,12}*1728b, {24,36}*1728c, {36,24}*1728c, {12,24}*1728d, {24,12}*1728c, {24,12}*1728d, {12,72}*1728c, {72,12}*1728c, {72,12}*1728d, {24,36}*1728d, {36,24}*1728d, {12,24}*1728f, {24,12}*1728e, {24,12}*1728f, {18,48}*1728b, {6,48}*1728c, {108,4}*1728b, {54,4}*1728b, {108,4}*1728c, {54,8}*1728b, {54,8}*1728c, {9,6}*1728, {9,24}*1728, {3,6}*1728, {3,24}*1728, {6,48}*1728f, {48,6}*1728f, {12,24}*1728o, {24,12}*1728o, {12,24}*1728p, {24,12}*1728p, {12,12}*1728h, {12,36}*1728c, {36,12}*1728c, {6,36}*1728b, {36,6}*1728a, {36,6}*1728b, {18,12}*1728a, {6,72}*1728b, {18,6}*1728a, {72,6}*1728b, {6,72}*1728c, {36,6}*1728c, {72,6}*1728c, {12,36}*1728d, {18,12}*1728b, {36,12}*1728d, {12,36}*1728e, {36,12}*1728e, {36,12}*1728f, {12,18}*1728c, {18,12}*1728c, {36,12}*1728g, {12,12}*1728i, {12,12}*1728j, {12,12}*1728l, {6,12}*1728b, {12,6}*1728a, {12,6}*1728b, {12,12}*1728m, {18,24}*1728b, {18,24}*1728c, {18,24}*1728d, {24,18}*1728c, {6,12}*1728c, {6,24}*1728b, {6,6}*1728b, {6,24}*1728c, {6,24}*1728d, {24,6}*1728c, {18,24}*1728e, {24,18}*1728e, {6,24}*1728e, {12,6}*1728d, {24,6}*1728e, {12,36}*1728h, {18,12}*1728d, {36,12}*1728h, {6,12}*1728e, {6,12}*1728f, {12,12}*1728o, {12,12}*1728p, {24,4}*1728e, {24,4}*1728f, {12,8}*1728e, {24,4}*1728g, {24,4}*1728h, {12,8}*1728f, {6,16}*1728b, {12,8}*1728g, {12,8}*1728h, {12,4}*1728c, {12,4}*1728d, {48,6}*1728h, {12,12}*1728s, {24,12}*1728u, {12,24}*1728v, {12,24}*1728w, {24,12}*1728x, {9,12}*1728, {3,12}*1728, {18,6}*1728b, {6,6}*1728c, {6,12}*1728g, {6,24}*1728f, {12,6}*1728g, {24,6}*1728f, {6,6}*1728f, {6,24}*1728g, {24,6}*1728g, {12,12}*1728v, {12,12}*1728w, {6,12}*1728h, {6,12}*1728i, {12,6}*1728h, {12,6}*1728i, {12,12}*1728x, {12,12}*1728y, {6,4}*1728, {12,4}*1728e, {12,12}*1728aa
145-fold covers : {435,2}*1740
146-fold covers : {6,146}*1752, {438,2}*1752
147-fold covers : {441,2}*1764, {147,6}*1764, {9,14}*1764, {63,14}*1764, {3,6}*1764, {3,42}*1764, {21,42}*1764
148-fold covers : {12,74}*1776, {6,148}*1776a, {444,2}*1776, {222,4}*1776a, {111,4}*1776
149-fold covers : {447,2}*1788
150-fold covers : {18,50}*1800, {450,2}*1800, {6,150}*1800a, {6,150}*1800b, {150,6}*1800b, {150,6}*1800c, {18,10}*1800a, {18,10}*1800b, {90,10}*1800a, {90,10}*1800b, {90,10}*1800c, {6,6}*1800b, {6,30}*1800a, {6,30}*1800b, {30,6}*1800a, {6,6}*1800d, {6,30}*1800c, {6,30}*1800d, {30,6}*1800d, {30,30}*1800a, {30,30}*1800b, {30,30}*1800d, {30,30}*1800f, {30,30}*1800g, {30,30}*1800i
151-fold covers : {453,2}*1812
152-fold covers : {24,38}*1824, {6,152}*1824, {12,76}*1824, {228,4}*1824a, {456,2}*1824, {114,8}*1824, {57,8}*1824, {6,76}*1824, {114,4}*1824
153-fold covers : {459,2}*1836, {153,6}*1836, {51,6}*1836
154-fold covers : {42,22}*1848, {66,14}*1848, {6,154}*1848, {462,2}*1848
155-fold covers : {465,2}*1860
156-fold covers : {36,26}*1872, {18,52}*1872a, {468,2}*1872, {234,4}*1872a, {117,4}*1872, {6,156}*1872a, {12,78}*1872a, {12,78}*1872b, {78,12}*1872b, {6,156}*1872b, {156,6}*1872b, {156,6}*1872c, {78,12}*1872c, {39,12}*1872, {39,6}*1872
157-fold covers : {471,2}*1884
158-fold covers : {6,158}*1896, {474,2}*1896
159-fold covers : {477,2}*1908, {159,6}*1908
160-fold covers : {60,8}*1920a, {120,4}*1920a, {12,40}*1920a, {24,20}*1920a, {120,8}*1920a, {120,8}*1920b, {120,8}*1920c, {24,40}*1920a, {24,40}*1920b, {24,40}*1920c, {120,8}*1920d, {24,40}*1920d, {60,16}*1920a, {240,4}*1920a, {12,80}*1920a, {48,20}*1920a, {60,16}*1920b, {240,4}*1920b, {12,80}*1920b, {48,20}*1920b, {60,4}*1920a, {120,4}*1920b, {60,8}*1920b, {12,40}*1920b, {24,20}*1920b, {12,20}*1920a, {30,32}*1920, {480,2}*1920, {96,10}*1920, {6,160}*1920, {15,8}*1920a, {30,8}*1920a, {6,40}*1920a, {12,40}*1920e, {12,40}*1920f, {6,40}*1920b, {6,20}*1920a, {6,40}*1920c, {24,20}*1920c, {24,20}*1920d, {6,40}*1920d, {6,20}*1920b, {12,20}*1920b, {12,20}*1920c, {12,40}*1920g, {12,40}*1920h, {24,20}*1920e, {24,20}*1920f, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {30,4}*1920a, {30,8}*1920d, {30,8}*1920e, {30,8}*1920f, {60,8}*1920g, {60,8}*1920h, {120,4}*1920c, {120,4}*1920d, {30,8}*1920g, {60,4}*1920e, {120,4}*1920e, {30,4}*1920b, {120,4}*1920f, {15,20}*1920a, {15,20}*1920b, {15,10}*1920, {30,10}*1920a, {15,8}*1920b, {15,4}*1920a, {15,8}*1920c, {30,4}*1920c, {12,10}*1920a, {30,10}*1920b, {30,4}*1920d
161-fold covers : {483,2}*1932
162-fold covers : {486,2}*1944, {18,18}*1944a, {18,18}*1944c, {6,6}*1944a, {18,6}*1944a, {6,18}*1944b, {18,18}*1944d, {6,18}*1944c, {18,6}*1944c, {18,6}*1944d, {18,18}*1944f, {6,18}*1944e, {18,6}*1944e, {18,6}*1944f, {18,18}*1944h, {18,18}*1944i, {18,18}*1944k, {18,18}*1944l, {18,18}*1944m, {18,18}*1944o, {18,54}*1944a, {54,18}*1944a, {54,18}*1944b, {6,54}*1944b, {54,6}*1944a, {54,6}*1944b, {6,18}*1944g, {18,6}*1944g, {18,6}*1944h, {18,18}*1944q, {18,18}*1944s, {18,18}*1944t, {18,18}*1944u, {18,18}*1944v, {18,18}*1944x, {18,18}*1944y, {18,18}*1944z, {6,18}*1944j, {18,6}*1944i, {18,6}*1944j, {18,18}*1944ab, {6,54}*1944d, {54,6}*1944c, {54,6}*1944d, {6,54}*1944f, {54,6}*1944e, {54,6}*1944f, {6,162}*1944a, {162,6}*1944a, {162,6}*1944b, {6,6}*1944b, {6,18}*1944k, {6,18}*1944l, {18,6}*1944l, {18,18}*1944ad, {18,18}*1944ae, {18,18}*1944af, {6,18}*1944m, {6,18}*1944n, {18,6}*1944m, {18,6}*1944n, {6,18}*1944o, {18,6}*1944o, {6,6}*1944d, {6,6}*1944e, {6,6}*1944f, {6,54}*1944g, {54,6}*1944g, {6,6}*1944g, {6,6}*1944h, {6,18}*1944p, {6,18}*1944q, {18,6}*1944p, {18,6}*1944q, {6,18}*1944r, {6,18}*1944s, {18,6}*1944r, {18,6}*1944s, {6,6}*1944i, {6,6}*1944j, {6,18}*1944t, {6,18}*1944u, {18,6}*1944t, {18,6}*1944u
163-fold covers : {489,2}*1956
164-fold covers : {12,82}*1968, {6,164}*1968a, {492,2}*1968, {246,4}*1968a, {123,4}*1968
165-fold covers : {495,2}*1980, {165,6}*1980
166-fold covers : {6,166}*1992, {498,2}*1992
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(5)!(2,3);
s1 := Sym(5)!(1,2);
s2 := Sym(5)!(4,5);
poly := sub<Sym(5)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1 >;
to this polytope