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