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Polytope of Type {12,12,2}

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

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