Polytope of Type {2,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6}*24
if this polytope has a name.
Group : SmallGroup(24,14)
Rank : 3
Schlafli Type : {2,6}
Number of vertices, edges, etc : 2, 6, 6
Order of s0s1s2 : 6
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,2} of size 48
{2,6,3} of size 72
{2,6,4} of size 96
{2,6,3} of size 96
{2,6,4} of size 96
{2,6,4} of size 96
{2,6,4} of size 144
{2,6,6} of size 144
{2,6,6} of size 144
{2,6,6} of size 144
{2,6,8} of size 192
{2,6,4} of size 192
{2,6,6} of size 192
{2,6,9} of size 216
{2,6,3} of size 216
{2,6,6} of size 216
{2,6,4} of size 240
{2,6,5} of size 240
{2,6,6} of size 240
{2,6,5} of size 240
{2,6,5} of size 240
{2,6,10} of size 240
{2,6,12} of size 288
{2,6,12} of size 288
{2,6,12} of size 288
{2,6,3} of size 288
{2,6,12} of size 288
{2,6,4} of size 288
{2,6,14} of size 336
{2,6,15} of size 360
{2,6,16} of size 384
{2,6,4} of size 384
{2,6,6} of size 384
{2,6,3} of size 384
{2,6,8} of size 384
{2,6,4} of size 384
{2,6,12} of size 384
{2,6,8} of size 384
{2,6,12} of size 384
{2,6,6} of size 384
{2,6,8} of size 384
{2,6,4} of size 432
{2,6,12} of size 432
{2,6,12} of size 432
{2,6,18} of size 432
{2,6,18} of size 432
{2,6,6} of size 432
{2,6,6} of size 432
{2,6,6} of size 432
{2,6,12} of size 432
{2,6,6} of size 432
{2,6,20} of size 480
{2,6,4} of size 480
{2,6,4} of size 480
{2,6,4} of size 480
{2,6,5} of size 480
{2,6,6} of size 480
{2,6,6} of size 480
{2,6,6} of size 480
{2,6,10} of size 480
{2,6,10} of size 480
{2,6,5} of size 480
{2,6,10} of size 480
{2,6,10} of size 480
{2,6,10} of size 480
{2,6,10} of size 480
{2,6,15} of size 480
{2,6,20} of size 480
{2,6,21} of size 504
{2,6,22} of size 528
{2,6,24} of size 576
{2,6,24} of size 576
{2,6,24} of size 576
{2,6,8} of size 576
{2,6,6} of size 576
{2,6,6} of size 576
{2,6,12} of size 576
{2,6,12} of size 576
{2,6,3} of size 600
{2,6,10} of size 600
{2,6,26} of size 624
{2,6,9} of size 648
{2,6,18} of size 648
{2,6,27} of size 648
{2,6,6} of size 648
{2,6,6} of size 648
{2,6,9} of size 648
{2,6,9} of size 648
{2,6,9} of size 648
{2,6,18} of size 648
{2,6,3} of size 648
{2,6,18} of size 648
{2,6,28} of size 672
{2,6,4} of size 672
{2,6,6} of size 672
{2,6,7} of size 672
{2,6,8} of size 672
{2,6,8} of size 672
{2,6,21} of size 672
{2,6,28} of size 672
{2,6,15} of size 720
{2,6,20} of size 720
{2,6,30} of size 720
{2,6,30} of size 720
{2,6,30} of size 720
{2,6,32} of size 768
{2,6,8} of size 768
{2,6,6} of size 768
{2,6,6} of size 768
{2,6,8} of size 768
{2,6,8} of size 768
{2,6,6} of size 768
{2,6,6} of size 768
{2,6,8} of size 768
{2,6,8} of size 768
{2,6,4} of size 768
{2,6,6} of size 768
{2,6,8} of size 768
{2,6,12} of size 768
{2,6,8} of size 768
{2,6,24} of size 768
{2,6,4} of size 768
{2,6,24} of size 768
{2,6,33} of size 792
{2,6,34} of size 816
{2,6,36} of size 864
{2,6,36} of size 864
{2,6,12} of size 864
{2,6,12} of size 864
{2,6,12} of size 864
{2,6,9} of size 864
{2,6,36} of size 864
{2,6,3} of size 864
{2,6,12} of size 864
{2,6,4} of size 864
{2,6,12} of size 864
{2,6,12} of size 864
{2,6,12} of size 864
{2,6,4} of size 864
{2,6,12} of size 864
{2,6,12} of size 864
{2,6,38} of size 912
{2,6,39} of size 936
{2,6,40} of size 960
{2,6,5} of size 960
{2,6,8} of size 960
{2,6,8} of size 960
{2,6,10} of size 960
{2,6,12} of size 960
{2,6,12} of size 960
{2,6,20} of size 960
{2,6,20} of size 960
{2,6,4} of size 960
{2,6,6} of size 960
{2,6,10} of size 960
{2,6,10} of size 960
{2,6,20} of size 960
{2,6,30} of size 960
{2,6,28} of size 1008
{2,6,42} of size 1008
{2,6,42} of size 1008
{2,6,42} of size 1008
{2,6,44} of size 1056
{2,6,33} of size 1056
{2,6,44} of size 1056
{2,6,45} of size 1080
{2,6,15} of size 1080
{2,6,30} of size 1080
{2,6,46} of size 1104
{2,6,48} of size 1152
{2,6,48} of size 1152
{2,6,48} of size 1152
{2,6,16} of size 1152
{2,6,3} of size 1152
{2,6,24} of size 1152
{2,6,12} of size 1152
{2,6,12} of size 1152
{2,6,12} of size 1152
{2,6,24} of size 1152
{2,6,6} of size 1152
{2,6,6} of size 1152
{2,6,24} of size 1152
{2,6,24} of size 1152
{2,6,12} of size 1152
{2,6,24} of size 1152
{2,6,12} of size 1152
{2,6,12} of size 1152
{2,6,6} of size 1152
{2,6,6} of size 1152
{2,6,6} of size 1152
{2,6,3} of size 1176
{2,6,14} of size 1176
{2,6,50} of size 1200
{2,6,5} of size 1200
{2,6,6} of size 1200
{2,6,6} of size 1200
{2,6,10} of size 1200
{2,6,10} of size 1200
{2,6,51} of size 1224
{2,6,52} of size 1248
{2,6,39} of size 1248
{2,6,52} of size 1248
{2,6,18} of size 1296
{2,6,18} of size 1296
{2,6,54} of size 1296
{2,6,54} of size 1296
{2,6,6} of size 1296
{2,6,6} of size 1296
{2,6,18} of size 1296
{2,6,18} of size 1296
{2,6,18} of size 1296
{2,6,18} of size 1296
{2,6,6} of size 1296
{2,6,6} of size 1296
{2,6,18} of size 1296
{2,6,18} of size 1296
{2,6,36} of size 1296
{2,6,12} of size 1296
{2,6,36} of size 1296
{2,6,36} of size 1296
{2,6,18} of size 1296
{2,6,6} of size 1296
{2,6,6} of size 1296
{2,6,6} of size 1296
{2,6,5} of size 1320
{2,6,6} of size 1320
{2,6,56} of size 1344
{2,6,4} of size 1344
{2,6,4} of size 1344
{2,6,4} of size 1344
{2,6,6} of size 1344
{2,6,6} of size 1344
{2,6,6} of size 1344
{2,6,7} of size 1344
{2,6,7} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,8} of size 1344
{2,6,14} of size 1344
{2,6,14} of size 1344
{2,6,28} of size 1344
{2,6,42} of size 1344
{2,6,57} of size 1368
{2,6,58} of size 1392
{2,6,60} of size 1440
{2,6,60} of size 1440
{2,6,60} of size 1440
{2,6,5} of size 1440
{2,6,6} of size 1440
{2,6,4} of size 1440
{2,6,6} of size 1440
{2,6,6} of size 1440
{2,6,6} of size 1440
{2,6,10} of size 1440
{2,6,12} of size 1440
{2,6,12} of size 1440
{2,6,15} of size 1440
{2,6,15} of size 1440
{2,6,10} of size 1440
{2,6,10} of size 1440
{2,6,15} of size 1440
{2,6,15} of size 1440
{2,6,30} of size 1440
{2,6,30} of size 1440
{2,6,15} of size 1440
{2,6,60} of size 1440
{2,6,20} of size 1440
{2,6,62} of size 1488
{2,6,63} of size 1512
{2,6,21} of size 1512
{2,6,42} of size 1512
{2,6,44} of size 1584
{2,6,66} of size 1584
{2,6,66} of size 1584
{2,6,66} of size 1584
{2,6,68} of size 1632
{2,6,51} of size 1632
{2,6,68} of size 1632
{2,6,69} of size 1656
{2,6,35} of size 1680
{2,6,70} of size 1680
{2,6,72} of size 1728
{2,6,72} of size 1728
{2,6,24} of size 1728
{2,6,24} of size 1728
{2,6,24} of size 1728
{2,6,8} of size 1728
{2,6,24} of size 1728
{2,6,24} of size 1728
{2,6,24} of size 1728
{2,6,18} of size 1728
{2,6,36} of size 1728
{2,6,6} of size 1728
{2,6,6} of size 1728
{2,6,12} of size 1728
{2,6,12} of size 1728
{2,6,8} of size 1728
{2,6,24} of size 1728
{2,6,24} of size 1728
{2,6,6} of size 1728
{2,6,12} of size 1728
{2,6,74} of size 1776
{2,6,75} of size 1800
{2,6,3} of size 1800
{2,6,30} of size 1800
{2,6,76} of size 1824
{2,6,57} of size 1824
{2,6,76} of size 1824
{2,6,52} of size 1872
{2,6,78} of size 1872
{2,6,78} of size 1872
{2,6,78} of size 1872
{2,6,80} of size 1920
{2,6,15} of size 1920
{2,6,40} of size 1920
{2,6,20} of size 1920
{2,6,60} of size 1920
{2,6,30} of size 1920
{2,6,40} of size 1920
{2,6,40} of size 1920
{2,6,60} of size 1920
{2,6,24} of size 1920
{2,6,24} of size 1920
{2,6,40} of size 1920
{2,6,40} of size 1920
{2,6,12} of size 1920
{2,6,4} of size 1920
{2,6,20} of size 1920
{2,6,20} of size 1920
{2,6,24} of size 1920
{2,6,24} of size 1920
{2,6,8} of size 1920
{2,6,10} of size 1920
{2,6,6} of size 1920
{2,6,8} of size 1920
{2,6,12} of size 1920
{2,6,20} of size 1920
{2,6,20} of size 1920
{2,6,10} of size 1920
{2,6,5} of size 1920
{2,6,6} of size 1944
{2,6,9} of size 1944
{2,6,9} of size 1944
{2,6,18} of size 1944
{2,6,9} of size 1944
{2,6,18} of size 1944
{2,6,27} of size 1944
{2,6,54} of size 1944
{2,6,9} of size 1944
{2,6,18} of size 1944
{2,6,9} of size 1944
{2,6,18} of size 1944
{2,6,27} of size 1944
{2,6,54} of size 1944
{2,6,27} of size 1944
{2,6,54} of size 1944
{2,6,81} of size 1944
{2,6,3} of size 1944
{2,6,18} of size 1944
{2,6,82} of size 1968
Vertex Figure Of :
{2,2,6} of size 48
{3,2,6} of size 72
{4,2,6} of size 96
{5,2,6} of size 120
{6,2,6} of size 144
{7,2,6} of size 168
{8,2,6} of size 192
{9,2,6} of size 216
{10,2,6} of size 240
{11,2,6} of size 264
{12,2,6} of size 288
{13,2,6} of size 312
{14,2,6} of size 336
{15,2,6} of size 360
{16,2,6} of size 384
{17,2,6} of size 408
{18,2,6} of size 432
{19,2,6} of size 456
{20,2,6} of size 480
{21,2,6} of size 504
{22,2,6} of size 528
{23,2,6} of size 552
{24,2,6} of size 576
{25,2,6} of size 600
{26,2,6} of size 624
{27,2,6} of size 648
{28,2,6} of size 672
{29,2,6} of size 696
{30,2,6} of size 720
{31,2,6} of size 744
{32,2,6} of size 768
{33,2,6} of size 792
{34,2,6} of size 816
{35,2,6} of size 840
{36,2,6} of size 864
{37,2,6} of size 888
{38,2,6} of size 912
{39,2,6} of size 936
{40,2,6} of size 960
{41,2,6} of size 984
{42,2,6} of size 1008
{43,2,6} of size 1032
{44,2,6} of size 1056
{45,2,6} of size 1080
{46,2,6} of size 1104
{47,2,6} of size 1128
{48,2,6} of size 1152
{49,2,6} of size 1176
{50,2,6} of size 1200
{51,2,6} of size 1224
{52,2,6} of size 1248
{53,2,6} of size 1272
{54,2,6} of size 1296
{55,2,6} of size 1320
{56,2,6} of size 1344
{57,2,6} of size 1368
{58,2,6} of size 1392
{59,2,6} of size 1416
{60,2,6} of size 1440
{61,2,6} of size 1464
{62,2,6} of size 1488
{63,2,6} of size 1512
{65,2,6} of size 1560
{66,2,6} of size 1584
{67,2,6} of size 1608
{68,2,6} of size 1632
{69,2,6} of size 1656
{70,2,6} of size 1680
{71,2,6} of size 1704
{72,2,6} of size 1728
{73,2,6} of size 1752
{74,2,6} of size 1776
{75,2,6} of size 1800
{76,2,6} of size 1824
{77,2,6} of size 1848
{78,2,6} of size 1872
{79,2,6} of size 1896
{80,2,6} of size 1920
{81,2,6} of size 1944
{82,2,6} of size 1968
{83,2,6} of size 1992
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3}*12
3-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12}*48, {4,6}*48a
3-fold covers : {2,18}*72, {6,6}*72a, {6,6}*72b
4-fold covers : {4,12}*96a, {2,24}*96, {8,6}*96, {4,6}*96
5-fold covers : {10,6}*120, {2,30}*120
6-fold covers : {2,36}*144, {4,18}*144a, {6,12}*144a, {6,12}*144b, {12,6}*144a, {12,6}*144c
7-fold covers : {14,6}*168, {2,42}*168
8-fold covers : {4,24}*192a, {4,12}*192a, {4,24}*192b, {8,12}*192a, {8,12}*192b, {2,48}*192, {16,6}*192, {4,12}*192b, {4,6}*192b, {4,12}*192c, {8,6}*192b, {8,6}*192c
9-fold covers : {2,54}*216, {6,18}*216a, {6,18}*216b, {18,6}*216a, {6,6}*216a, {6,6}*216b, {6,6}*216d
10-fold covers : {10,12}*240, {20,6}*240a, {2,60}*240, {4,30}*240a
11-fold covers : {22,6}*264, {2,66}*264
12-fold covers : {4,36}*288a, {2,72}*288, {8,18}*288, {6,24}*288a, {6,24}*288b, {24,6}*288a, {12,12}*288a, {12,12}*288b, {24,6}*288c, {4,18}*288, {6,6}*288a, {6,12}*288a, {12,6}*288a, {12,6}*288b
13-fold covers : {26,6}*312, {2,78}*312
14-fold covers : {14,12}*336, {28,6}*336a, {2,84}*336, {4,42}*336a
15-fold covers : {10,18}*360, {2,90}*360, {30,6}*360a, {6,30}*360b, {6,30}*360c, {30,6}*360b
16-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, {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
17-fold covers : {34,6}*408, {2,102}*408
18-fold covers : {2,108}*432, {4,54}*432a, {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, {6,12}*432g, {12,6}*432g, {4,6}*432b, {4,12}*432b, {6,12}*432i
19-fold covers : {38,6}*456, {2,114}*456
20-fold covers : {10,24}*480, {40,6}*480, {20,12}*480, {4,60}*480a, {2,120}*480, {8,30}*480, {20,6}*480c, {4,30}*480
21-fold covers : {14,18}*504, {2,126}*504, {42,6}*504a, {6,42}*504b, {6,42}*504c, {42,6}*504b
22-fold covers : {22,12}*528, {44,6}*528a, {2,132}*528, {4,66}*528a
23-fold covers : {46,6}*552, {2,138}*552
24-fold covers : {4,72}*576a, {4,36}*576a, {4,72}*576b, {8,36}*576a, {8,36}*576b, {2,144}*576, {16,18}*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, {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
25-fold covers : {50,6}*600, {2,150}*600, {10,6}*600a, {10,6}*600b, {10,30}*600a, {10,30}*600b, {10,30}*600c
26-fold covers : {26,12}*624, {52,6}*624a, {2,156}*624, {4,78}*624a
27-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
28-fold covers : {14,24}*672, {56,6}*672, {28,12}*672, {4,84}*672a, {2,168}*672, {8,42}*672, {28,6}*672, {4,42}*672
29-fold covers : {58,6}*696, {2,174}*696
30-fold covers : {10,36}*720, {20,18}*720a, {2,180}*720, {4,90}*720a, {60,6}*720a, {30,12}*720a, {12,30}*720b, {30,12}*720b, {6,60}*720b, {6,60}*720c, {60,6}*720b, {12,30}*720c
31-fold covers : {62,6}*744, {2,186}*744
32-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, {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
33-fold covers : {22,18}*792, {2,198}*792, {66,6}*792a, {6,66}*792b, {6,66}*792c, {66,6}*792b
34-fold covers : {34,12}*816, {68,6}*816a, {2,204}*816, {4,102}*816a
35-fold covers : {14,30}*840, {10,42}*840, {70,6}*840, {2,210}*840
36-fold covers : {4,108}*864a, {2,216}*864, {8,54}*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, {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
37-fold covers : {74,6}*888, {2,222}*888
38-fold covers : {38,12}*912, {76,6}*912a, {2,228}*912, {4,114}*912a
39-fold covers : {26,18}*936, {2,234}*936, {78,6}*936a, {6,78}*936b, {6,78}*936c, {78,6}*936b
40-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, {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
41-fold covers : {82,6}*984, {2,246}*984
42-fold covers : {14,36}*1008, {28,18}*1008a, {2,252}*1008, {4,126}*1008a, {84,6}*1008a, {42,12}*1008a, {12,42}*1008b, {42,12}*1008b, {6,84}*1008b, {6,84}*1008c, {84,6}*1008b, {12,42}*1008c
43-fold covers : {86,6}*1032, {2,258}*1032
44-fold covers : {22,24}*1056, {88,6}*1056, {44,12}*1056, {4,132}*1056a, {2,264}*1056, {8,66}*1056, {44,6}*1056, {4,66}*1056
45-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
46-fold covers : {46,12}*1104, {92,6}*1104a, {2,276}*1104, {4,138}*1104a
47-fold covers : {94,6}*1128, {2,282}*1128
48-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, {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, {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, {12,6}*1152j, {12,12}*1152t, {6,6}*1152j, {6,6}*1152k
49-fold covers : {98,6}*1176, {2,294}*1176, {14,6}*1176a, {14,6}*1176b, {14,42}*1176a, {14,42}*1176b, {14,42}*1176c
50-fold covers : {50,12}*1200, {100,6}*1200a, {2,300}*1200, {4,150}*1200a, {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, {10,12}*1200c
51-fold covers : {34,18}*1224, {2,306}*1224, {102,6}*1224a, {6,102}*1224b, {6,102}*1224c, {102,6}*1224b
52-fold covers : {26,24}*1248, {104,6}*1248, {52,12}*1248, {4,156}*1248a, {2,312}*1248, {8,78}*1248, {52,6}*1248, {4,78}*1248
53-fold covers : {106,6}*1272, {2,318}*1272
54-fold covers : {2,324}*1296, {4,162}*1296a, {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, {6,36}*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, {12,6}*1296s, {12,12}*1296f, {6,12}*1296t, {6,12}*1296u, {12,6}*1296t, {12,12}*1296g
55-fold covers : {22,30}*1320, {10,66}*1320, {110,6}*1320, {2,330}*1320
56-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, {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
57-fold covers : {38,18}*1368, {2,342}*1368, {114,6}*1368a, {6,114}*1368b, {6,114}*1368c, {114,6}*1368b
58-fold covers : {58,12}*1392, {116,6}*1392a, {2,348}*1392, {4,174}*1392a
59-fold covers : {118,6}*1416, {2,354}*1416
60-fold covers : {10,72}*1440, {40,18}*1440, {20,36}*1440, {4,180}*1440a, {2,360}*1440, {8,90}*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, {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
61-fold covers : {122,6}*1464, {2,366}*1464
62-fold covers : {62,12}*1488, {124,6}*1488a, {2,372}*1488, {4,186}*1488a
63-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
65-fold covers : {26,30}*1560, {10,78}*1560, {130,6}*1560, {2,390}*1560
66-fold covers : {22,36}*1584, {44,18}*1584a, {2,396}*1584, {4,198}*1584a, {132,6}*1584a, {66,12}*1584a, {12,66}*1584b, {66,12}*1584b, {6,132}*1584b, {6,132}*1584c, {132,6}*1584b, {12,66}*1584c
67-fold covers : {134,6}*1608, {2,402}*1608
68-fold covers : {34,24}*1632, {136,6}*1632, {68,12}*1632, {4,204}*1632a, {2,408}*1632, {8,102}*1632, {68,6}*1632, {4,102}*1632
69-fold covers : {46,18}*1656, {2,414}*1656, {138,6}*1656a, {6,138}*1656b, {6,138}*1656c, {138,6}*1656b
70-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
71-fold covers : {142,6}*1704, {2,426}*1704
72-fold covers : {4,216}*1728a, {4,108}*1728a, {4,216}*1728b, {8,108}*1728a, {8,108}*1728b, {2,432}*1728, {16,54}*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, {6,48}*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, {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
73-fold covers : {146,6}*1752, {2,438}*1752
74-fold covers : {74,12}*1776, {148,6}*1776a, {2,444}*1776, {4,222}*1776a
75-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
76-fold covers : {38,24}*1824, {152,6}*1824, {76,12}*1824, {4,228}*1824a, {2,456}*1824, {8,114}*1824, {76,6}*1824, {4,114}*1824
77-fold covers : {22,42}*1848, {14,66}*1848, {154,6}*1848, {2,462}*1848
78-fold covers : {26,36}*1872, {52,18}*1872a, {2,468}*1872, {4,234}*1872a, {156,6}*1872a, {78,12}*1872a, {12,78}*1872b, {78,12}*1872b, {6,156}*1872b, {6,156}*1872c, {156,6}*1872b, {12,78}*1872c
79-fold covers : {158,6}*1896, {2,474}*1896
80-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, {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, {10,12}*1920a, {10,30}*1920b, {4,30}*1920d
81-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
82-fold covers : {82,12}*1968, {164,6}*1968a, {2,492}*1968, {4,246}*1968a
83-fold covers : {166,6}*1992, {2,498}*1992
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(8)!(1,2);
s1 := Sym(8)!(5,6)(7,8);
s2 := Sym(8)!(3,7)(4,5)(6,8);
poly := sub<Sym(8)|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*s1*s2*s1*s2*s1*s2 >;
to this polytope