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