Polytope of Type {6,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157559)
Rank : 4
Schlafli Type : {6,4,6}
Number of vertices, edges, etc : 24, 48, 48, 6
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {6,4,6}*576b
   3-fold quotients : {6,4,2}*384b
   4-fold quotients : {6,4,6}*288, {3,4,6}*288
   6-fold quotients : {6,4,2}*192
   8-fold quotients : {6,2,6}*144
   12-fold quotients : {2,4,6}*96a, {6,4,2}*96a, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   24-fold quotients : {3,4,2}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   36-fold quotients : {2,4,2}*32
   48-fold quotients : {2,2,3}*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 := (  3,  4)(  7,  8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)
( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 39, 40)
( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)( 54, 66)
( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 75, 76)( 79, 80)
( 83, 84)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,101)( 90,102)( 91,104)
( 92,103)( 93,105)( 94,106)( 95,108)( 96,107)(111,112)(115,116)(119,120)
(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)
(129,141)(130,142)(131,144)(132,143);;
s1 := (  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 17)(  6, 20)(  7, 19)(  8, 18)
(  9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)( 37, 49)
( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 45, 57)
( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73,121)( 74,124)
( 75,123)( 76,122)( 77,125)( 78,128)( 79,127)( 80,126)( 81,129)( 82,132)
( 83,131)( 84,130)( 85,109)( 86,112)( 87,111)( 88,110)( 89,113)( 90,116)
( 91,115)( 92,114)( 93,117)( 94,120)( 95,119)( 96,118)( 97,133)( 98,136)
( 99,135)(100,134)(101,137)(102,140)(103,139)(104,138)(105,141)(106,144)
(107,143)(108,142);;
s2 := (  1, 74)(  2, 73)(  3, 76)(  4, 75)(  5, 82)(  6, 81)(  7, 84)(  8, 83)
(  9, 78)( 10, 77)( 11, 80)( 12, 79)( 13, 86)( 14, 85)( 15, 88)( 16, 87)
( 17, 94)( 18, 93)( 19, 96)( 20, 95)( 21, 90)( 22, 89)( 23, 92)( 24, 91)
( 25, 98)( 26, 97)( 27,100)( 28, 99)( 29,106)( 30,105)( 31,108)( 32,107)
( 33,102)( 34,101)( 35,104)( 36,103)( 37,110)( 38,109)( 39,112)( 40,111)
( 41,118)( 42,117)( 43,120)( 44,119)( 45,114)( 46,113)( 47,116)( 48,115)
( 49,122)( 50,121)( 51,124)( 52,123)( 53,130)( 54,129)( 55,132)( 56,131)
( 57,126)( 58,125)( 59,128)( 60,127)( 61,134)( 62,133)( 63,136)( 64,135)
( 65,142)( 66,141)( 67,144)( 68,143)( 69,138)( 70,137)( 71,140)( 72,139);;
s3 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)( 13, 17)( 14, 18)( 15, 19)( 16, 20)
( 25, 29)( 26, 30)( 27, 31)( 28, 32)( 37, 41)( 38, 42)( 39, 43)( 40, 44)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 61, 65)( 62, 66)( 63, 67)( 64, 68)
( 73, 77)( 74, 78)( 75, 79)( 76, 80)( 85, 89)( 86, 90)( 87, 91)( 88, 92)
( 97,101)( 98,102)( 99,103)(100,104)(109,113)(110,114)(111,115)(112,116)
(121,125)(122,126)(123,127)(124,128)(133,137)(134,138)(135,139)(136,140);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope