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