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Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157640)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 24, 144, 48
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6}*576b
   3-fold quotients : {2,6,12}*384a
   4-fold quotients : {2,6,12}*288c, {2,3,6}*288
   6-fold quotients : {2,6,6}*192
   8-fold quotients : {2,6,6}*144c
   12-fold quotients : {2,6,4}*96a, {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,3}*48, {2,6,2}*48
   36-fold quotients : {2,2,4}*32
   48-fold quotients : {2,3,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 27)( 16, 29)( 17, 28)
( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)( 25, 32)
( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)( 52, 65)
( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)( 60, 69)
( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 87, 99)
( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)( 95,103)
( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)(118,122)
(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)(130,146)
(131,139)(132,141)(133,140)(134,142);;
s2 := (  3, 91)(  4, 92)(  5, 94)(  6, 93)(  7, 87)(  8, 88)(  9, 90)( 10, 89)
( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 79)( 16, 80)( 17, 82)( 18, 81)
( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 83)( 24, 84)( 25, 86)( 26, 85)
( 27,103)( 28,104)( 29,106)( 30,105)( 31, 99)( 32,100)( 33,102)( 34,101)
( 35,107)( 36,108)( 37,110)( 38,109)( 39,127)( 40,128)( 41,130)( 42,129)
( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)( 50,133)
( 51,115)( 52,116)( 53,118)( 54,117)( 55,111)( 56,112)( 57,114)( 58,113)
( 59,119)( 60,120)( 61,122)( 62,121)( 63,139)( 64,140)( 65,142)( 66,141)
( 67,135)( 68,136)( 69,138)( 70,137)( 71,143)( 72,144)( 73,146)( 74,145);;
s3 := (  3,  6)(  7, 10)( 11, 14)( 15, 30)( 16, 28)( 17, 29)( 18, 27)( 19, 34)
( 20, 32)( 21, 33)( 22, 31)( 23, 38)( 24, 36)( 25, 37)( 26, 35)( 39, 42)
( 43, 46)( 47, 50)( 51, 66)( 52, 64)( 53, 65)( 54, 63)( 55, 70)( 56, 68)
( 57, 69)( 58, 67)( 59, 74)( 60, 72)( 61, 73)( 62, 71)( 75,114)( 76,112)
( 77,113)( 78,111)( 79,118)( 80,116)( 81,117)( 82,115)( 83,122)( 84,120)
( 85,121)( 86,119)( 87,138)( 88,136)( 89,137)( 90,135)( 91,142)( 92,140)
( 93,141)( 94,139)( 95,146)( 96,144)( 97,145)( 98,143)( 99,126)(100,124)
(101,125)(102,123)(103,130)(104,128)(105,129)(106,127)(107,134)(108,132)
(109,133)(110,131);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 27)( 16, 29)
( 17, 28)( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)
( 25, 32)( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)
( 52, 65)( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)
( 60, 69)( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)
( 87, 99)( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)
( 95,103)( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)
(118,122)(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)
(130,146)(131,139)(132,141)(133,140)(134,142);
s2 := Sym(146)!(  3, 91)(  4, 92)(  5, 94)(  6, 93)(  7, 87)(  8, 88)(  9, 90)
( 10, 89)( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 79)( 16, 80)( 17, 82)
( 18, 81)( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 83)( 24, 84)( 25, 86)
( 26, 85)( 27,103)( 28,104)( 29,106)( 30,105)( 31, 99)( 32,100)( 33,102)
( 34,101)( 35,107)( 36,108)( 37,110)( 38,109)( 39,127)( 40,128)( 41,130)
( 42,129)( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)
( 50,133)( 51,115)( 52,116)( 53,118)( 54,117)( 55,111)( 56,112)( 57,114)
( 58,113)( 59,119)( 60,120)( 61,122)( 62,121)( 63,139)( 64,140)( 65,142)
( 66,141)( 67,135)( 68,136)( 69,138)( 70,137)( 71,143)( 72,144)( 73,146)
( 74,145);
s3 := Sym(146)!(  3,  6)(  7, 10)( 11, 14)( 15, 30)( 16, 28)( 17, 29)( 18, 27)
( 19, 34)( 20, 32)( 21, 33)( 22, 31)( 23, 38)( 24, 36)( 25, 37)( 26, 35)
( 39, 42)( 43, 46)( 47, 50)( 51, 66)( 52, 64)( 53, 65)( 54, 63)( 55, 70)
( 56, 68)( 57, 69)( 58, 67)( 59, 74)( 60, 72)( 61, 73)( 62, 71)( 75,114)
( 76,112)( 77,113)( 78,111)( 79,118)( 80,116)( 81,117)( 82,115)( 83,122)
( 84,120)( 85,121)( 86,119)( 87,138)( 88,136)( 89,137)( 90,135)( 91,142)
( 92,140)( 93,141)( 94,139)( 95,146)( 96,144)( 97,145)( 98,143)( 99,126)
(100,124)(101,125)(102,123)(103,130)(104,128)(105,129)(106,127)(107,134)
(108,132)(109,133)(110,131);
poly := sub<Sym(146)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >; 
 

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