Polytope of Type {4,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,99269)
Rank : 4
Schlafli Type : {4,12,6}
Number of vertices, edges, etc : 8, 48, 72, 6
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {4,12,6}*576c
   3-fold quotients : {4,4,6}*384a
   4-fold quotients : {4,6,6}*288c, {2,12,6}*288c
   6-fold quotients : {4,4,6}*192
   8-fold quotients : {4,6,3}*144, {2,6,6}*144b
   9-fold quotients : {4,4,2}*128
   12-fold quotients : {2,4,6}*96a, {4,2,6}*96
   16-fold quotients : {2,6,3}*72
   18-fold quotients : {4,4,2}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)
( 27, 36)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)
( 62, 71)( 63, 72)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)( 96,105)
( 97,106)( 98,107)( 99,108)(127,136)(128,137)(129,138)(130,139)(131,140)
(132,141)(133,142)(134,143)(135,144);;
s1 := (  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 38, 42)( 39, 44)( 41, 45)( 47, 51)
( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)( 68, 72)
( 73, 91)( 74, 96)( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)
( 81, 95)( 82,100)( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)
( 89,102)( 90,104)(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)
(115,133)(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)
(123,137)(124,142)(125,138)(126,140);;
s2 := (  1,110)(  2,109)(  3,111)(  4,116)(  5,115)(  6,117)(  7,113)(  8,112)
(  9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)( 16,122)
( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)( 24,135)
( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)( 32,142)
( 33,144)( 34,140)( 35,139)( 36,141)( 37, 74)( 38, 73)( 39, 75)( 40, 80)
( 41, 79)( 42, 81)( 43, 77)( 44, 76)( 45, 78)( 46, 83)( 47, 82)( 48, 84)
( 49, 89)( 50, 88)( 51, 90)( 52, 86)( 53, 85)( 54, 87)( 55, 92)( 56, 91)
( 57, 93)( 58, 98)( 59, 97)( 60, 99)( 61, 95)( 62, 94)( 63, 96)( 64,101)
( 65,100)( 66,102)( 67,107)( 68,106)( 69,108)( 70,104)( 71,103)( 72,105);;
s3 := (  1, 37)(  2, 39)(  3, 38)(  4, 43)(  5, 45)(  6, 44)(  7, 40)(  8, 42)
(  9, 41)( 10, 46)( 11, 48)( 12, 47)( 13, 52)( 14, 54)( 15, 53)( 16, 49)
( 17, 51)( 18, 50)( 19, 55)( 20, 57)( 21, 56)( 22, 61)( 23, 63)( 24, 62)
( 25, 58)( 26, 60)( 27, 59)( 28, 64)( 29, 66)( 30, 65)( 31, 70)( 32, 72)
( 33, 71)( 34, 67)( 35, 69)( 36, 68)( 73,109)( 74,111)( 75,110)( 76,115)
( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)
( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,127)( 92,129)
( 93,128)( 94,133)( 95,135)( 96,134)( 97,130)( 98,132)( 99,131)(100,136)
(101,138)(102,137)(103,142)(104,144)(105,143)(106,139)(107,141)(108,140);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(144)!( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)
( 26, 35)( 27, 36)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)
( 61, 70)( 62, 71)( 63, 72)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)
( 96,105)( 97,106)( 98,107)( 99,108)(127,136)(128,137)(129,138)(130,139)
(131,140)(132,141)(133,142)(134,143)(135,144);
s1 := Sym(144)!(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 38, 42)( 39, 44)( 41, 45)
( 47, 51)( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)
( 68, 72)( 73, 91)( 74, 96)( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)
( 80, 93)( 81, 95)( 82,100)( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)
( 88,106)( 89,102)( 90,104)(109,127)(110,132)(111,134)(112,130)(113,135)
(114,128)(115,133)(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)
(122,144)(123,137)(124,142)(125,138)(126,140);
s2 := Sym(144)!(  1,110)(  2,109)(  3,111)(  4,116)(  5,115)(  6,117)(  7,113)
(  8,112)(  9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)
( 16,122)( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)
( 24,135)( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)
( 32,142)( 33,144)( 34,140)( 35,139)( 36,141)( 37, 74)( 38, 73)( 39, 75)
( 40, 80)( 41, 79)( 42, 81)( 43, 77)( 44, 76)( 45, 78)( 46, 83)( 47, 82)
( 48, 84)( 49, 89)( 50, 88)( 51, 90)( 52, 86)( 53, 85)( 54, 87)( 55, 92)
( 56, 91)( 57, 93)( 58, 98)( 59, 97)( 60, 99)( 61, 95)( 62, 94)( 63, 96)
( 64,101)( 65,100)( 66,102)( 67,107)( 68,106)( 69,108)( 70,104)( 71,103)
( 72,105);
s3 := Sym(144)!(  1, 37)(  2, 39)(  3, 38)(  4, 43)(  5, 45)(  6, 44)(  7, 40)
(  8, 42)(  9, 41)( 10, 46)( 11, 48)( 12, 47)( 13, 52)( 14, 54)( 15, 53)
( 16, 49)( 17, 51)( 18, 50)( 19, 55)( 20, 57)( 21, 56)( 22, 61)( 23, 63)
( 24, 62)( 25, 58)( 26, 60)( 27, 59)( 28, 64)( 29, 66)( 30, 65)( 31, 70)
( 32, 72)( 33, 71)( 34, 67)( 35, 69)( 36, 68)( 73,109)( 74,111)( 75,110)
( 76,115)( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)
( 84,119)( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,127)
( 92,129)( 93,128)( 94,133)( 95,135)( 96,134)( 97,130)( 98,132)( 99,131)
(100,136)(101,138)(102,137)(103,142)(104,144)(105,143)(106,139)(107,141)
(108,140);
poly := sub<Sym(144)|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, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1 >;

References : None.
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