Polytope of Type {2,2,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3}*24
if this polytope has a name.
Group : SmallGroup(24,14)
Rank : 4
Schlafli Type : {2,2,3}
Number of vertices, edges, etc : 2, 2, 3, 3
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Projective
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,3,2} of size 48
{2,2,3,3} of size 96
{2,2,3,4} of size 96
{2,2,3,6} of size 144
{2,2,3,4} of size 192
{2,2,3,6} of size 192
{2,2,3,5} of size 240
{2,2,3,8} of size 384
{2,2,3,12} of size 384
{2,2,3,6} of size 432
{2,2,3,5} of size 480
{2,2,3,10} of size 480
{2,2,3,10} of size 480
{2,2,3,6} of size 576
{2,2,3,12} of size 576
{2,2,3,6} of size 768
{2,2,3,8} of size 768
{2,2,3,10} of size 960
{2,2,3,12} of size 1152
{2,2,3,24} of size 1152
{2,2,3,6} of size 1200
{2,2,3,10} of size 1200
{2,2,3,6} of size 1296
{2,2,3,18} of size 1296
{2,2,3,7} of size 1344
{2,2,3,8} of size 1344
{2,2,3,8} of size 1344
{2,2,3,10} of size 1440
{2,2,3,15} of size 1440
{2,2,3,6} of size 1728
{2,2,3,12} of size 1728
{2,2,3,20} of size 1920
Vertex Figure Of :
{2,2,2,3} of size 48
{3,2,2,3} of size 72
{4,2,2,3} of size 96
{5,2,2,3} of size 120
{6,2,2,3} of size 144
{7,2,2,3} of size 168
{8,2,2,3} of size 192
{9,2,2,3} of size 216
{10,2,2,3} of size 240
{11,2,2,3} of size 264
{12,2,2,3} of size 288
{13,2,2,3} of size 312
{14,2,2,3} of size 336
{15,2,2,3} of size 360
{16,2,2,3} of size 384
{17,2,2,3} of size 408
{18,2,2,3} of size 432
{19,2,2,3} of size 456
{20,2,2,3} of size 480
{21,2,2,3} of size 504
{22,2,2,3} of size 528
{23,2,2,3} of size 552
{24,2,2,3} of size 576
{25,2,2,3} of size 600
{26,2,2,3} of size 624
{27,2,2,3} of size 648
{28,2,2,3} of size 672
{29,2,2,3} of size 696
{30,2,2,3} of size 720
{31,2,2,3} of size 744
{32,2,2,3} of size 768
{33,2,2,3} of size 792
{34,2,2,3} of size 816
{35,2,2,3} of size 840
{36,2,2,3} of size 864
{37,2,2,3} of size 888
{38,2,2,3} of size 912
{39,2,2,3} of size 936
{40,2,2,3} of size 960
{41,2,2,3} of size 984
{42,2,2,3} of size 1008
{43,2,2,3} of size 1032
{44,2,2,3} of size 1056
{45,2,2,3} of size 1080
{46,2,2,3} of size 1104
{47,2,2,3} of size 1128
{48,2,2,3} of size 1152
{49,2,2,3} of size 1176
{50,2,2,3} of size 1200
{51,2,2,3} of size 1224
{52,2,2,3} of size 1248
{53,2,2,3} of size 1272
{54,2,2,3} of size 1296
{55,2,2,3} of size 1320
{56,2,2,3} of size 1344
{57,2,2,3} of size 1368
{58,2,2,3} of size 1392
{59,2,2,3} of size 1416
{60,2,2,3} of size 1440
{61,2,2,3} of size 1464
{62,2,2,3} of size 1488
{63,2,2,3} of size 1512
{65,2,2,3} of size 1560
{66,2,2,3} of size 1584
{67,2,2,3} of size 1608
{68,2,2,3} of size 1632
{69,2,2,3} of size 1656
{70,2,2,3} of size 1680
{71,2,2,3} of size 1704
{72,2,2,3} of size 1728
{73,2,2,3} of size 1752
{74,2,2,3} of size 1776
{75,2,2,3} of size 1800
{76,2,2,3} of size 1824
{77,2,2,3} of size 1848
{78,2,2,3} of size 1872
{79,2,2,3} of size 1896
{80,2,2,3} of size 1920
{81,2,2,3} of size 1944
{82,2,2,3} of size 1968
{83,2,2,3} of size 1992
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,3}*48, {2,2,6}*48
3-fold covers : {2,2,9}*72, {2,6,3}*72, {6,2,3}*72
4-fold covers : {8,2,3}*96, {2,2,12}*96, {2,4,6}*96a, {4,2,6}*96, {2,4,3}*96
5-fold covers : {10,2,3}*120, {2,2,15}*120
6-fold covers : {4,2,9}*144, {2,2,18}*144, {12,2,3}*144, {4,6,3}*144, {2,6,6}*144a, {2,6,6}*144b, {6,2,6}*144
7-fold covers : {14,2,3}*168, {2,2,21}*168
8-fold covers : {16,2,3}*192, {2,4,12}*192a, {4,2,12}*192, {4,4,6}*192, {2,2,24}*192, {2,8,6}*192, {8,2,6}*192, {4,4,3}*192b, {2,8,3}*192, {2,4,6}*192
9-fold covers : {2,2,27}*216, {2,6,9}*216, {6,2,9}*216, {18,2,3}*216, {2,6,3}*216, {6,6,3}*216a, {6,6,3}*216b
10-fold covers : {20,2,3}*240, {4,2,15}*240, {2,10,6}*240, {10,2,6}*240, {2,2,30}*240
11-fold covers : {22,2,3}*264, {2,2,33}*264
12-fold covers : {8,2,9}*288, {2,2,36}*288, {2,4,18}*288a, {4,2,18}*288, {24,2,3}*288, {8,6,3}*288, {2,4,9}*288, {2,6,12}*288a, {2,6,12}*288b, {2,12,6}*288a, {6,2,12}*288, {12,2,6}*288, {4,6,6}*288a, {6,4,6}*288, {4,6,6}*288c, {2,12,6}*288c, {6,4,3}*288, {2,6,3}*288, {2,12,3}*288
13-fold covers : {26,2,3}*312, {2,2,39}*312
14-fold covers : {28,2,3}*336, {4,2,21}*336, {2,14,6}*336, {14,2,6}*336, {2,2,42}*336
15-fold covers : {10,2,9}*360, {2,2,45}*360, {10,6,3}*360, {2,6,15}*360, {6,2,15}*360, {30,2,3}*360
16-fold covers : {32,2,3}*384, {4,4,12}*384, {2,4,24}*384a, {2,4,12}*384a, {2,4,24}*384b, {2,8,12}*384a, {2,8,12}*384b, {4,2,24}*384, {8,2,12}*384, {4,8,6}*384a, {8,4,6}*384a, {4,8,6}*384b, {8,4,6}*384b, {4,4,6}*384a, {2,2,48}*384, {2,16,6}*384, {16,2,6}*384, {4,4,3}*384b, {2,8,3}*384, {4,8,3}*384, {8,4,3}*384, {2,4,12}*384b, {4,4,6}*384d, {2,4,6}*384b, {2,4,12}*384c, {2,8,6}*384b, {2,8,6}*384c
17-fold covers : {34,2,3}*408, {2,2,51}*408
18-fold covers : {4,2,27}*432, {2,2,54}*432, {36,2,3}*432, {12,2,9}*432, {12,6,3}*432a, {4,6,9}*432, {4,6,3}*432a, {2,6,18}*432a, {2,6,18}*432b, {2,18,6}*432a, {6,2,18}*432, {18,2,6}*432, {6,6,6}*432a, {2,6,6}*432a, {2,6,6}*432b, {12,6,3}*432b, {4,6,3}*432b, {6,6,6}*432b, {6,6,6}*432c, {6,6,6}*432d, {6,6,6}*432g, {2,6,6}*432d
19-fold covers : {38,2,3}*456, {2,2,57}*456
20-fold covers : {40,2,3}*480, {8,2,15}*480, {2,10,12}*480, {10,2,12}*480, {2,20,6}*480a, {20,2,6}*480, {4,10,6}*480, {10,4,6}*480, {2,2,60}*480, {2,4,30}*480a, {4,2,30}*480, {10,4,3}*480, {2,4,15}*480
21-fold covers : {14,2,9}*504, {2,2,63}*504, {14,6,3}*504, {2,6,21}*504, {6,2,21}*504, {42,2,3}*504
22-fold covers : {44,2,3}*528, {4,2,33}*528, {2,22,6}*528, {22,2,6}*528, {2,2,66}*528
23-fold covers : {46,2,3}*552, {2,2,69}*552
24-fold covers : {16,2,9}*576, {2,4,36}*576a, {4,2,36}*576, {4,4,18}*576, {2,2,72}*576, {2,8,18}*576, {8,2,18}*576, {48,2,3}*576, {16,6,3}*576, {4,4,9}*576b, {2,8,9}*576, {12,2,12}*576, {4,12,6}*576a, {6,4,12}*576, {12,4,6}*576, {4,6,12}*576a, {2,6,24}*576a, {2,6,24}*576b, {2,24,6}*576a, {6,2,24}*576, {24,2,6}*576, {6,8,6}*576, {8,6,6}*576a, {2,12,12}*576a, {2,12,12}*576b, {4,6,12}*576b, {8,6,6}*576c, {2,24,6}*576c, {4,12,6}*576c, {2,4,18}*576, {12,4,3}*576, {2,12,3}*576, {2,24,3}*576, {6,8,3}*576, {4,6,3}*576a, {4,12,3}*576, {4,6,6}*576a, {6,4,6}*576a, {6,4,6}*576b, {6,6,6}*576b, {2,6,6}*576a, {2,6,12}*576a, {2,12,6}*576a, {2,12,6}*576b
25-fold covers : {50,2,3}*600, {2,2,75}*600, {2,10,3}*600, {2,10,15}*600, {10,2,15}*600
26-fold covers : {52,2,3}*624, {4,2,39}*624, {2,26,6}*624, {26,2,6}*624, {2,2,78}*624
27-fold covers : {2,2,81}*648, {2,18,9}*648, {18,2,9}*648, {6,6,9}*648a, {2,6,9}*648a, {18,6,3}*648a, {2,6,27}*648, {6,2,27}*648, {54,2,3}*648, {6,6,3}*648a, {2,6,9}*648b, {6,6,3}*648b, {2,6,9}*648c, {2,6,9}*648d, {2,6,3}*648, {2,18,3}*648, {6,6,9}*648b, {18,6,3}*648b, {6,6,3}*648c, {6,6,3}*648d, {6,6,3}*648e
28-fold covers : {56,2,3}*672, {8,2,21}*672, {2,14,12}*672, {14,2,12}*672, {2,28,6}*672a, {28,2,6}*672, {4,14,6}*672, {14,4,6}*672, {2,2,84}*672, {2,4,42}*672a, {4,2,42}*672, {14,4,3}*672, {2,4,21}*672
29-fold covers : {58,2,3}*696, {2,2,87}*696
30-fold covers : {20,2,9}*720, {4,2,45}*720, {2,10,18}*720, {10,2,18}*720, {2,2,90}*720, {20,6,3}*720, {12,2,15}*720, {60,2,3}*720, {4,6,15}*720, {6,10,6}*720, {10,6,6}*720a, {10,6,6}*720b, {2,30,6}*720a, {2,6,30}*720b, {2,6,30}*720c, {2,30,6}*720b, {6,2,30}*720, {30,2,6}*720
31-fold covers : {62,2,3}*744, {2,2,93}*744
32-fold covers : {64,2,3}*768, {4,8,6}*768a, {8,4,6}*768a, {2,8,12}*768a, {2,4,24}*768a, {8,8,6}*768a, {8,8,6}*768b, {8,8,6}*768c, {2,8,24}*768a, {2,8,24}*768b, {2,8,24}*768c, {8,8,6}*768d, {2,8,24}*768d, {8,2,24}*768, {8,4,12}*768a, {4,4,24}*768a, {8,4,12}*768b, {4,4,24}*768b, {4,8,12}*768a, {4,4,12}*768a, {4,4,12}*768b, {4,8,12}*768b, {4,8,12}*768c, {4,8,12}*768d, {4,16,6}*768a, {16,4,6}*768a, {2,16,12}*768a, {2,4,48}*768a, {4,16,6}*768b, {16,4,6}*768b, {2,16,12}*768b, {2,4,48}*768b, {4,4,6}*768a, {4,8,6}*768b, {8,4,6}*768b, {2,4,12}*768a, {2,4,24}*768b, {2,8,12}*768b, {16,2,12}*768, {4,2,48}*768, {2,32,6}*768, {32,2,6}*768, {2,2,96}*768, {2,8,3}*768, {2,8,6}*768a, {4,8,3}*768a, {4,8,3}*768b, {8,8,3}*768, {4,4,3}*768a, {4,4,6}*768b, {4,8,3}*768c, {4,8,3}*768d, {4,4,3}*768b, {4,4,3}*768c, {4,8,3}*768e, {4,8,3}*768f, {16,4,3}*768, {2,4,12}*768d, {4,4,6}*768e, {4,4,12}*768e, {4,4,12}*768f, {2,8,6}*768d, {2,8,6}*768e, {4,4,6}*768f, {2,4,6}*768a, {2,8,12}*768e, {2,8,12}*768f, {2,4,24}*768c, {2,4,24}*768d, {4,8,6}*768c, {2,8,6}*768f, {2,8,12}*768g, {2,8,12}*768h, {8,4,6}*768c, {2,8,6}*768g, {4,8,6}*768d, {2,4,6}*768b, {2,4,24}*768e, {2,4,12}*768e, {2,4,24}*768f
33-fold covers : {22,2,9}*792, {2,2,99}*792, {22,6,3}*792, {2,6,33}*792, {6,2,33}*792, {66,2,3}*792
34-fold covers : {68,2,3}*816, {4,2,51}*816, {2,34,6}*816, {34,2,6}*816, {2,2,102}*816
35-fold covers : {14,2,15}*840, {10,2,21}*840, {70,2,3}*840, {2,2,105}*840
36-fold covers : {8,2,27}*864, {2,2,108}*864, {2,4,54}*864a, {4,2,54}*864, {72,2,3}*864, {24,2,9}*864, {24,6,3}*864a, {8,6,9}*864, {8,6,3}*864a, {2,4,27}*864, {2,6,36}*864a, {2,6,36}*864b, {2,36,6}*864a, {6,2,36}*864, {36,2,6}*864, {2,12,18}*864a, {2,18,12}*864a, {12,2,18}*864, {18,2,12}*864, {6,6,12}*864a, {12,6,6}*864a, {2,6,12}*864a, {2,6,12}*864b, {2,12,6}*864b, {4,6,18}*864a, {4,18,6}*864a, {6,4,18}*864, {18,4,6}*864, {4,6,6}*864b, {6,12,6}*864a, {4,6,18}*864b, {2,12,18}*864b, {4,6,6}*864c, {2,12,6}*864c, {24,6,3}*864b, {2,6,9}*864, {18,4,3}*864, {6,4,9}*864, {2,12,9}*864, {2,6,3}*864, {2,12,3}*864, {6,12,3}*864a, {8,6,3}*864b, {6,6,12}*864b, {6,6,12}*864c, {6,6,12}*864d, {6,12,6}*864b, {6,12,6}*864c, {12,6,6}*864b, {12,6,6}*864d, {6,6,12}*864e, {12,6,6}*864e, {2,6,12}*864g, {2,12,6}*864g, {4,6,6}*864h, {6,12,6}*864f, {6,12,6}*864g, {12,6,6}*864f, {6,6,3}*864, {6,12,3}*864b, {4,4,6}*864b, {4,6,6}*864j, {4,6,6}*864k, {6,4,6}*864b, {2,4,6}*864b, {2,4,12}*864b, {2,6,12}*864i
37-fold covers : {74,2,3}*888, {2,2,111}*888
38-fold covers : {76,2,3}*912, {4,2,57}*912, {2,38,6}*912, {38,2,6}*912, {2,2,114}*912
39-fold covers : {26,2,9}*936, {2,2,117}*936, {26,6,3}*936, {2,6,39}*936, {6,2,39}*936, {78,2,3}*936
40-fold covers : {80,2,3}*960, {16,2,15}*960, {20,2,12}*960, {10,4,12}*960, {4,20,6}*960, {20,4,6}*960, {4,10,12}*960, {2,10,24}*960, {10,2,24}*960, {2,40,6}*960, {40,2,6}*960, {8,10,6}*960, {10,8,6}*960, {2,20,12}*960, {2,4,60}*960a, {4,2,60}*960, {4,4,30}*960, {2,2,120}*960, {2,8,30}*960, {8,2,30}*960, {20,4,3}*960, {10,8,3}*960, {4,4,15}*960b, {2,8,15}*960, {10,4,6}*960, {2,20,6}*960c, {2,4,30}*960
41-fold covers : {82,2,3}*984, {2,2,123}*984
42-fold covers : {28,2,9}*1008, {4,2,63}*1008, {2,14,18}*1008, {14,2,18}*1008, {2,2,126}*1008, {28,6,3}*1008, {12,2,21}*1008, {84,2,3}*1008, {4,6,21}*1008, {6,14,6}*1008, {14,6,6}*1008a, {14,6,6}*1008b, {2,42,6}*1008a, {2,6,42}*1008b, {2,6,42}*1008c, {2,42,6}*1008b, {6,2,42}*1008, {42,2,6}*1008
43-fold covers : {86,2,3}*1032, {2,2,129}*1032
44-fold covers : {88,2,3}*1056, {8,2,33}*1056, {2,22,12}*1056, {22,2,12}*1056, {2,44,6}*1056a, {44,2,6}*1056, {4,22,6}*1056, {22,4,6}*1056, {2,2,132}*1056, {2,4,66}*1056a, {4,2,66}*1056, {22,4,3}*1056, {2,4,33}*1056
45-fold covers : {10,2,27}*1080, {2,2,135}*1080, {10,6,9}*1080, {10,6,3}*1080, {2,6,45}*1080, {6,2,45}*1080, {90,2,3}*1080, {18,2,15}*1080, {30,2,9}*1080, {6,6,15}*1080a, {2,6,15}*1080, {30,6,3}*1080a, {6,6,15}*1080b, {30,6,3}*1080b
46-fold covers : {92,2,3}*1104, {4,2,69}*1104, {2,46,6}*1104, {46,2,6}*1104, {2,2,138}*1104
47-fold covers : {94,2,3}*1128, {2,2,141}*1128
48-fold covers : {32,2,9}*1152, {32,6,3}*1152, {96,2,3}*1152, {4,4,36}*1152, {4,12,12}*1152b, {4,12,12}*1152c, {12,4,12}*1152, {4,8,18}*1152a, {8,4,18}*1152a, {2,8,36}*1152a, {2,4,72}*1152a, {6,8,12}*1152a, {8,12,6}*1152b, {12,8,6}*1152a, {4,24,6}*1152a, {8,12,6}*1152c, {4,24,6}*1152c, {6,4,24}*1152a, {24,4,6}*1152a, {2,12,24}*1152a, {2,12,24}*1152b, {2,24,12}*1152a, {2,24,12}*1152c, {4,8,18}*1152b, {8,4,18}*1152b, {2,8,36}*1152b, {2,4,72}*1152b, {6,8,12}*1152b, {8,12,6}*1152e, {12,8,6}*1152b, {4,24,6}*1152d, {8,12,6}*1152f, {4,24,6}*1152f, {6,4,24}*1152b, {24,4,6}*1152b, {2,12,24}*1152d, {2,12,24}*1152e, {2,24,12}*1152d, {2,24,12}*1152f, {4,4,18}*1152a, {2,4,36}*1152a, {4,12,6}*1152b, {6,4,12}*1152a, {12,4,6}*1152a, {4,12,6}*1152c, {2,12,12}*1152a, {2,12,12}*1152b, {8,2,36}*1152, {4,2,72}*1152, {8,6,12}*1152b, {8,6,12}*1152c, {4,6,24}*1152b, {4,6,24}*1152c, {12,2,24}*1152, {24,2,12}*1152, {2,16,18}*1152, {16,2,18}*1152, {2,2,144}*1152, {6,16,6}*1152, {16,6,6}*1152a, {16,6,6}*1152c, {2,48,6}*1152a, {2,6,48}*1152b, {2,6,48}*1152c, {2,48,6}*1152b, {6,2,48}*1152, {48,2,6}*1152, {4,4,9}*1152b, {2,8,9}*1152, {4,8,9}*1152, {8,4,9}*1152, {2,4,36}*1152b, {4,4,18}*1152d, {2,4,18}*1152b, {2,4,36}*1152c, {2,8,18}*1152b, {2,8,18}*1152c, {2,6,3}*1152, {2,24,3}*1152, {12,8,3}*1152, {4,6,3}*1152a, {4,12,3}*1152a, {12,4,3}*1152, {6,8,3}*1152, {24,4,3}*1152, {8,6,3}*1152, {8,12,3}*1152, {4,12,3}*1152b, {4,24,3}*1152, {4,12,6}*1152e, {6,4,12}*1152b, {12,4,6}*1152b, {2,12,12}*1152d, {2,12,12}*1152f, {2,12,12}*1152g, {4,6,12}*1152a, {6,4,12}*1152c, {6,6,12}*1152a, {12,4,6}*1152c, {2,6,12}*1152a, {2,6,12}*1152b, {2,12,6}*1152b, {2,12,12}*1152i, {4,6,6}*1152d, {4,6,12}*1152b, {4,12,6}*1152g, {4,12,6}*1152h, {6,4,6}*1152a, {6,4,6}*1152b, {6,4,12}*1152d, {6,12,6}*1152b, {12,4,6}*1152d, {12,6,6}*1152b, {2,12,6}*1152c, {2,24,6}*1152b, {2,6,6}*1152a, {2,6,24}*1152c, {2,24,6}*1152c, {2,24,6}*1152d, {6,8,6}*1152a, {6,8,6}*1152b, {6,12,6}*1152d, {8,6,6}*1152b, {12,6,6}*1152c, {2,6,12}*1152d, {2,6,24}*1152e, {2,24,6}*1152e, {6,6,6}*1152b, {6,8,6}*1152c, {6,8,6}*1152d, {8,6,6}*1152d, {4,6,6}*1152f, {4,12,6}*1152j, {2,12,6}*1152e, {2,12,6}*1152f, {2,12,12}*1152j, {2,12,12}*1152k, {2,12,3}*1152, {4,6,3}*1152c, {6,4,3}*1152b, {2,6,6}*1152d
49-fold covers : {98,2,3}*1176, {2,2,147}*1176, {2,14,3}*1176, {2,14,21}*1176, {14,2,21}*1176
50-fold covers : {100,2,3}*1200, {4,2,75}*1200, {2,50,6}*1200, {50,2,6}*1200, {2,2,150}*1200, {4,10,3}*1200, {20,2,15}*1200, {4,10,15}*1200, {2,10,6}*1200a, {2,10,6}*1200b, {10,10,6}*1200a, {10,10,6}*1200b, {10,10,6}*1200c, {2,10,30}*1200a, {2,10,30}*1200b, {2,10,30}*1200c, {10,2,30}*1200
51-fold covers : {34,2,9}*1224, {2,2,153}*1224, {34,6,3}*1224, {2,6,51}*1224, {6,2,51}*1224, {102,2,3}*1224
52-fold covers : {104,2,3}*1248, {8,2,39}*1248, {2,26,12}*1248, {26,2,12}*1248, {2,52,6}*1248a, {52,2,6}*1248, {4,26,6}*1248, {26,4,6}*1248, {2,2,156}*1248, {2,4,78}*1248a, {4,2,78}*1248, {26,4,3}*1248, {2,4,39}*1248
53-fold covers : {106,2,3}*1272, {2,2,159}*1272
54-fold covers : {4,2,81}*1296, {2,2,162}*1296, {36,2,9}*1296, {12,6,9}*1296a, {36,6,3}*1296a, {12,2,27}*1296, {108,2,3}*1296, {12,6,3}*1296a, {12,6,3}*1296b, {4,18,9}*1296, {4,6,9}*1296a, {4,6,27}*1296, {4,6,9}*1296b, {4,6,9}*1296c, {4,6,9}*1296d, {4,6,3}*1296a, {4,18,3}*1296, {2,18,18}*1296a, {2,18,18}*1296b, {18,2,18}*1296, {6,6,18}*1296a, {18,6,6}*1296a, {2,6,18}*1296a, {2,6,18}*1296b, {2,18,6}*1296b, {2,6,54}*1296a, {2,6,54}*1296b, {2,54,6}*1296a, {6,2,54}*1296, {54,2,6}*1296, {6,6,6}*1296a, {6,6,6}*1296b, {2,6,6}*1296a, {2,6,6}*1296b, {2,6,18}*1296c, {2,6,18}*1296d, {2,6,18}*1296e, {2,6,18}*1296f, {2,18,6}*1296f, {2,6,6}*1296c, {2,6,18}*1296g, {2,18,6}*1296g, {2,18,6}*1296h, {36,6,3}*1296b, {12,6,9}*1296b, {12,6,3}*1296c, {12,6,3}*1296d, {12,6,3}*1296e, {4,6,9}*1296e, {6,6,18}*1296b, {6,6,18}*1296c, {6,6,18}*1296d, {6,6,18}*1296e, {6,18,6}*1296a, {6,18,6}*1296b, {18,6,6}*1296b, {18,6,6}*1296c, {2,6,18}*1296i, {18,6,6}*1296e, {2,18,6}*1296i, {6,6,6}*1296c, {6,6,6}*1296f, {6,6,6}*1296g, {6,6,6}*1296h, {6,6,6}*1296i, {6,6,6}*1296j, {6,6,6}*1296k, {2,6,6}*1296e, {6,6,6}*1296n, {2,6,6}*1296f, {6,6,6}*1296o, {2,6,6}*1296g, {6,6,6}*1296p, {4,6,3}*1296b, {12,6,3}*1296f, {6,6,6}*1296q, {6,6,6}*1296r, {6,6,6}*1296s
55-fold covers : {22,2,15}*1320, {10,2,33}*1320, {110,2,3}*1320, {2,2,165}*1320
56-fold covers : {112,2,3}*1344, {16,2,21}*1344, {28,2,12}*1344, {4,14,12}*1344, {14,4,12}*1344, {4,28,6}*1344, {28,4,6}*1344, {2,14,24}*1344, {14,2,24}*1344, {2,56,6}*1344, {56,2,6}*1344, {8,14,6}*1344, {14,8,6}*1344, {2,28,12}*1344, {2,4,84}*1344a, {4,2,84}*1344, {4,4,42}*1344, {2,2,168}*1344, {2,8,42}*1344, {8,2,42}*1344, {28,4,3}*1344, {14,8,3}*1344, {4,4,21}*1344b, {2,8,21}*1344, {14,4,6}*1344, {2,28,6}*1344, {2,4,42}*1344
57-fold covers : {38,2,9}*1368, {2,2,171}*1368, {38,6,3}*1368, {2,6,57}*1368, {6,2,57}*1368, {114,2,3}*1368
58-fold covers : {116,2,3}*1392, {4,2,87}*1392, {2,58,6}*1392, {58,2,6}*1392, {2,2,174}*1392
59-fold covers : {118,2,3}*1416, {2,2,177}*1416
60-fold covers : {40,2,9}*1440, {8,2,45}*1440, {2,10,36}*1440, {10,2,36}*1440, {2,20,18}*1440a, {20,2,18}*1440, {4,10,18}*1440, {10,4,18}*1440, {2,2,180}*1440, {2,4,90}*1440a, {4,2,90}*1440, {40,6,3}*1440, {24,2,15}*1440, {120,2,3}*1440, {8,6,15}*1440, {10,4,9}*1440, {2,4,45}*1440, {6,10,12}*1440, {10,6,12}*1440a, {10,6,12}*1440b, {10,12,6}*1440a, {12,10,6}*1440, {6,20,6}*1440, {20,6,6}*1440a, {20,6,6}*1440c, {2,60,6}*1440a, {2,30,12}*1440a, {4,30,6}*1440a, {10,12,6}*1440c, {2,12,30}*1440b, {2,30,12}*1440b, {12,2,30}*1440, {30,2,12}*1440, {2,6,60}*1440b, {2,6,60}*1440c, {2,60,6}*1440b, {6,2,60}*1440, {60,2,6}*1440, {4,6,30}*1440b, {4,30,6}*1440b, {6,4,30}*1440, {30,4,6}*1440, {4,6,30}*1440c, {2,12,30}*1440c, {2,4,15}*1440, {6,6,3}*1440b, {2,6,15}*1440a, {2,6,15}*1440d, {2,10,3}*1440b, {2,10,15}*1440, {10,6,3}*1440, {10,12,3}*1440, {6,4,15}*1440, {2,12,15}*1440, {2,6,15}*1440e, {30,4,3}*1440
61-fold covers : {122,2,3}*1464, {2,2,183}*1464
62-fold covers : {124,2,3}*1488, {4,2,93}*1488, {2,62,6}*1488, {62,2,6}*1488, {2,2,186}*1488
63-fold covers : {14,2,27}*1512, {2,2,189}*1512, {14,6,9}*1512, {14,6,3}*1512, {2,6,63}*1512, {6,2,63}*1512, {126,2,3}*1512, {18,2,21}*1512, {42,2,9}*1512, {6,6,21}*1512a, {2,6,21}*1512, {42,6,3}*1512a, {6,6,21}*1512b, {42,6,3}*1512b
65-fold covers : {26,2,15}*1560, {10,2,39}*1560, {130,2,3}*1560, {2,2,195}*1560
66-fold covers : {44,2,9}*1584, {4,2,99}*1584, {2,22,18}*1584, {22,2,18}*1584, {2,2,198}*1584, {44,6,3}*1584, {12,2,33}*1584, {132,2,3}*1584, {4,6,33}*1584, {6,22,6}*1584, {22,6,6}*1584a, {22,6,6}*1584b, {2,66,6}*1584a, {2,6,66}*1584b, {2,6,66}*1584c, {2,66,6}*1584b, {6,2,66}*1584, {66,2,6}*1584
67-fold covers : {134,2,3}*1608, {2,2,201}*1608
68-fold covers : {136,2,3}*1632, {8,2,51}*1632, {2,34,12}*1632, {34,2,12}*1632, {2,68,6}*1632a, {68,2,6}*1632, {4,34,6}*1632, {34,4,6}*1632, {2,2,204}*1632, {2,4,102}*1632a, {4,2,102}*1632, {34,4,3}*1632, {2,4,51}*1632
69-fold covers : {46,2,9}*1656, {2,2,207}*1656, {46,6,3}*1656, {2,6,69}*1656, {6,2,69}*1656, {138,2,3}*1656
70-fold covers : {28,2,15}*1680, {20,2,21}*1680, {140,2,3}*1680, {4,2,105}*1680, {10,14,6}*1680, {14,10,6}*1680, {2,14,30}*1680, {14,2,30}*1680, {2,10,42}*1680, {10,2,42}*1680, {2,70,6}*1680, {70,2,6}*1680, {2,2,210}*1680
71-fold covers : {142,2,3}*1704, {2,2,213}*1704
72-fold covers : {16,2,27}*1728, {2,4,108}*1728a, {4,2,108}*1728, {4,4,54}*1728, {2,2,216}*1728, {2,8,54}*1728, {8,2,54}*1728, {144,2,3}*1728, {48,2,9}*1728, {48,6,3}*1728a, {16,6,9}*1728, {16,6,3}*1728a, {4,4,27}*1728b, {2,8,27}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {4,6,36}*1728a, {4,18,12}*1728a, {4,12,18}*1728a, {12,4,18}*1728, {18,4,12}*1728, {4,36,6}*1728a, {6,4,36}*1728, {36,4,6}*1728, {4,6,12}*1728a, {4,12,6}*1728b, {6,12,12}*1728a, {12,12,6}*1728a, {2,6,72}*1728a, {2,6,72}*1728b, {2,72,6}*1728a, {6,2,72}*1728, {72,2,6}*1728, {2,18,24}*1728a, {2,24,18}*1728a, {18,2,24}*1728, {24,2,18}*1728, {6,6,24}*1728a, {24,6,6}*1728a, {2,6,24}*1728a, {2,6,24}*1728b, {2,24,6}*1728b, {6,8,18}*1728, {8,6,18}*1728a, {8,18,6}*1728a, {18,8,6}*1728, {6,24,6}*1728a, {8,6,6}*1728b, {2,12,36}*1728a, {2,12,36}*1728b, {2,36,12}*1728a, {4,6,36}*1728b, {2,12,12}*1728b, {2,12,12}*1728c, {4,6,12}*1728b, {8,6,18}*1728b, {2,24,18}*1728b, {8,6,6}*1728c, {2,24,6}*1728c, {4,12,18}*1728b, {4,12,6}*1728c, {2,4,54}*1728, {48,6,3}*1728b, {36,4,3}*1728, {2,12,9}*1728, {18,8,3}*1728, {4,6,9}*1728a, {12,4,9}*1728, {12,12,3}*1728a, {2,24,9}*1728, {2,12,3}*1728, {2,24,3}*1728, {6,8,9}*1728, {6,24,3}*1728a, {4,12,9}*1728, {4,6,3}*1728a, {4,12,3}*1728a, {16,6,3}*1728b, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728d, {6,24,6}*1728b, {6,24,6}*1728c, {24,6,6}*1728b, {24,6,6}*1728d, {6,6,24}*1728e, {24,6,6}*1728e, {2,6,24}*1728f, {2,24,6}*1728f, {12,6,12}*1728b, {12,6,12}*1728c, {12,6,12}*1728e, {12,6,12}*1728f, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728d, {12,12,6}*1728b, {12,12,6}*1728c, {12,12,6}*1728f, {6,24,6}*1728f, {6,24,6}*1728g, {8,6,6}*1728e, {24,6,6}*1728f, {2,12,12}*1728h, {4,12,6}*1728j, {6,12,12}*1728g, {12,12,6}*1728g, {4,6,12}*1728h, {4,6,18}*1728, {6,4,18}*1728a, {6,6,18}*1728, {18,4,6}*1728a, {2,6,18}*1728, {2,6,36}*1728, {2,36,6}*1728, {4,18,6}*1728a, {6,4,18}*1728b, {18,4,6}*1728b, {2,12,18}*1728a, {2,12,18}*1728b, {2,18,12}*1728a, {4,6,6}*1728b, {6,12,6}*1728a, {6,12,6}*1728b, {2,6,6}*1728b, {2,6,12}*1728b, {2,12,6}*1728a, {2,12,6}*1728b, {6,12,3}*1728, {6,24,3}*1728b, {12,6,3}*1728, {12,12,3}*1728b, {6,8,6}*1728a, {8,6,6}*1728f, {4,4,12}*1728b, {4,6,12}*1728k, {4,6,12}*1728l, {6,4,12}*1728a, {2,4,12}*1728c, {2,4,12}*1728d, {8,6,6}*1728g, {2,8,6}*1728b, {4,4,6}*1728b, {4,4,6}*1728c, {4,12,6}*1728n, {4,12,6}*1728o, {12,4,6}*1728b, {4,4,12}*1728c, {2,6,24}*1728h, {4,6,12}*1728n, {2,12,12}*1728l, {4,12,3}*1728b, {4,6,6}*1728c, {6,6,6}*1728a, {6,6,6}*1728d, {6,6,6}*1728f, {6,6,12}*1728a, {6,6,12}*1728b, {6,12,6}*1728e, {6,12,6}*1728f, {6,12,6}*1728g, {6,12,6}*1728h, {2,6,6}*1728c, {6,12,6}*1728i, {6,12,6}*1728j, {6,12,6}*1728l, {12,6,6}*1728a, {2,6,12}*1728c, {12,6,6}*1728b, {2,12,6}*1728c
73-fold covers : {146,2,3}*1752, {2,2,219}*1752
74-fold covers : {148,2,3}*1776, {4,2,111}*1776, {2,74,6}*1776, {74,2,6}*1776, {2,2,222}*1776
75-fold covers : {50,2,9}*1800, {2,2,225}*1800, {50,6,3}*1800, {2,6,75}*1800, {6,2,75}*1800, {150,2,3}*1800, {2,10,9}*1800, {2,10,45}*1800, {10,2,45}*1800, {6,10,3}*1800, {2,6,3}*1800, {2,30,3}*1800, {6,10,15}*1800, {10,6,15}*1800, {2,30,15}*1800, {30,2,15}*1800
76-fold covers : {152,2,3}*1824, {8,2,57}*1824, {2,38,12}*1824, {38,2,12}*1824, {2,76,6}*1824a, {76,2,6}*1824, {4,38,6}*1824, {38,4,6}*1824, {2,2,228}*1824, {2,4,114}*1824a, {4,2,114}*1824, {38,4,3}*1824, {2,4,57}*1824
77-fold covers : {22,2,21}*1848, {14,2,33}*1848, {154,2,3}*1848, {2,2,231}*1848
78-fold covers : {52,2,9}*1872, {4,2,117}*1872, {2,26,18}*1872, {26,2,18}*1872, {2,2,234}*1872, {52,6,3}*1872, {12,2,39}*1872, {156,2,3}*1872, {4,6,39}*1872, {6,26,6}*1872, {26,6,6}*1872a, {26,6,6}*1872b, {2,78,6}*1872a, {2,6,78}*1872b, {2,6,78}*1872c, {2,78,6}*1872b, {6,2,78}*1872, {78,2,6}*1872
79-fold covers : {158,2,3}*1896, {2,2,237}*1896
80-fold covers : {32,2,15}*1920, {160,2,3}*1920, {4,4,60}*1920, {4,20,12}*1920, {20,4,12}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {2,8,60}*1920a, {2,4,120}*1920a, {10,8,12}*1920a, {8,20,6}*1920a, {20,8,6}*1920a, {10,4,24}*1920a, {4,40,6}*1920a, {40,4,6}*1920a, {2,40,12}*1920a, {2,20,24}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {2,8,60}*1920b, {2,4,120}*1920b, {10,8,12}*1920b, {8,20,6}*1920b, {20,8,6}*1920b, {10,4,24}*1920b, {4,40,6}*1920b, {40,4,6}*1920b, {2,40,12}*1920b, {2,20,24}*1920b, {4,4,30}*1920a, {2,4,60}*1920a, {10,4,12}*1920a, {4,20,6}*1920a, {20,4,6}*1920a, {2,20,12}*1920a, {8,2,60}*1920, {4,2,120}*1920, {8,10,12}*1920, {4,10,24}*1920, {40,2,12}*1920, {20,2,24}*1920, {2,16,30}*1920, {16,2,30}*1920, {2,2,240}*1920, {10,16,6}*1920, {16,10,6}*1920, {2,10,48}*1920, {10,2,48}*1920, {2,80,6}*1920, {80,2,6}*1920, {20,8,3}*1920, {20,4,3}*1920, {10,8,3}*1920, {40,4,3}*1920, {4,4,15}*1920b, {2,8,15}*1920a, {4,8,15}*1920, {8,4,15}*1920, {10,4,12}*1920b, {2,20,12}*1920b, {20,4,6}*1920b, {2,20,6}*1920a, {4,20,6}*1920c, {10,4,6}*1920, {10,4,12}*1920c, {2,40,6}*1920b, {10,8,6}*1920a, {2,40,6}*1920c, {10,8,6}*1920b, {2,20,12}*1920c, {2,4,60}*1920b, {4,4,30}*1920d, {2,4,30}*1920b, {2,4,60}*1920c, {2,8,30}*1920b, {2,8,30}*1920c, {2,10,15}*1920, {2,4,15}*1920
81-fold covers : {2,2,243}*1944, {18,6,9}*1944a, {2,18,9}*1944a, {6,6,3}*1944a, {2,6,9}*1944a, {2,18,3}*1944a, {2,6,9}*1944b, {2,18,9}*1944b, {2,6,9}*1944c, {2,18,9}*1944c, {2,18,9}*1944d, {2,18,9}*1944e, {2,18,27}*1944, {18,2,27}*1944, {54,2,9}*1944, {6,6,27}*1944a, {2,6,27}*1944a, {54,6,3}*1944a, {6,6,9}*1944a, {2,6,9}*1944d, {18,6,3}*1944a, {2,18,9}*1944f, {2,18,9}*1944g, {2,18,9}*1944h, {2,18,9}*1944i, {6,6,9}*1944b, {2,6,9}*1944e, {18,6,3}*1944b, {2,18,9}*1944j, {2,6,27}*1944b, {2,6,27}*1944c, {2,6,81}*1944, {6,2,81}*1944, {162,2,3}*1944, {2,6,3}*1944, {2,18,3}*1944b, {6,18,9}*1944, {18,6,9}*1944b, {6,6,9}*1944c, {6,6,9}*1944d, {18,6,3}*1944c, {18,6,3}*1944d, {6,6,9}*1944e, {18,6,3}*1944e, {6,6,3}*1944b, {6,6,3}*1944c, {6,6,3}*1944d, {6,6,27}*1944b, {54,6,3}*1944b, {6,6,3}*1944e, {6,6,3}*1944f, {6,6,3}*1944g, {6,6,9}*1944f, {6,6,9}*1944g, {6,6,9}*1944h, {6,6,3}*1944h, {6,18,3}*1944
82-fold covers : {164,2,3}*1968, {4,2,123}*1968, {2,82,6}*1968, {82,2,6}*1968, {2,2,246}*1968
83-fold covers : {166,2,3}*1992, {2,2,249}*1992
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (6,7);;
s3 := (5,6);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(7)!(1,2);
s1 := Sym(7)!(3,4);
s2 := Sym(7)!(6,7);
s3 := Sym(7)!(5,6);
poly := sub<Sym(7)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3 >;
to this polytope