Polytope of Type {4,6,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4,3}*1152a
Also Known As : {{4,6|2},{6,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(1152,157559)
Rank : 5
Schlafli Type : {4,6,4,3}
Number of vertices, edges, etc : 4, 12, 24, 12, 6
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,6,4,3}*576
   3-fold quotients : {4,2,4,3}*384
   4-fold quotients : {4,6,2,3}*288a
   6-fold quotients : {4,2,4,3}*192, {2,2,4,3}*192
   8-fold quotients : {2,6,2,3}*144
   12-fold quotients : {4,2,2,3}*96, {2,2,4,3}*96
   16-fold quotients : {2,3,2,3}*72
   24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)
( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)
( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)
(105,141)(106,142)(107,143)(108,144);;
s1 := (  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 81)(  6, 82)(  7, 83)(  8, 84)
(  9, 77)( 10, 78)( 11, 79)( 12, 80)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 93)( 18, 94)( 19, 95)( 20, 96)( 21, 89)( 22, 90)( 23, 91)( 24, 92)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,105)( 30,106)( 31,107)( 32,108)
( 33,101)( 34,102)( 35,103)( 36,104)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,117)( 42,118)( 43,119)( 44,120)( 45,113)( 46,114)( 47,115)( 48,116)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,129)( 54,130)( 55,131)( 56,132)
( 57,125)( 58,126)( 59,127)( 60,128)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,141)( 66,142)( 67,143)( 68,144)( 69,137)( 70,138)( 71,139)( 72,140);;
s2 := (  1,  7)(  2,  8)(  3,  5)(  4,  6)(  9, 11)( 10, 12)( 13, 19)( 14, 20)
( 15, 17)( 16, 18)( 21, 23)( 22, 24)( 25, 31)( 26, 32)( 27, 29)( 28, 30)
( 33, 35)( 34, 36)( 37, 43)( 38, 44)( 39, 41)( 40, 42)( 45, 47)( 46, 48)
( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 57, 59)( 58, 60)( 61, 67)( 62, 68)
( 63, 65)( 64, 66)( 69, 71)( 70, 72)( 73, 79)( 74, 80)( 75, 77)( 76, 78)
( 81, 83)( 82, 84)( 85, 91)( 86, 92)( 87, 89)( 88, 90)( 93, 95)( 94, 96)
( 97,103)( 98,104)( 99,101)(100,102)(105,107)(106,108)(109,115)(110,116)
(111,113)(112,114)(117,119)(118,120)(121,127)(122,128)(123,125)(124,126)
(129,131)(130,132)(133,139)(134,140)(135,137)(136,138)(141,143)(142,144);;
s3 := (  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);;
s4 := (  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, 85)( 74, 88)
( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)( 82, 96)
( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)(111,123)
(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)(119,131)
(120,130)(134,136)(138,140)(142,144);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(144)!( 73,109)( 74,110)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)
( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)
( 96,132)( 97,133)( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)
(104,140)(105,141)(106,142)(107,143)(108,144);
s1 := Sym(144)!(  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 81)(  6, 82)(  7, 83)
(  8, 84)(  9, 77)( 10, 78)( 11, 79)( 12, 80)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 93)( 18, 94)( 19, 95)( 20, 96)( 21, 89)( 22, 90)( 23, 91)
( 24, 92)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,105)( 30,106)( 31,107)
( 32,108)( 33,101)( 34,102)( 35,103)( 36,104)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,117)( 42,118)( 43,119)( 44,120)( 45,113)( 46,114)( 47,115)
( 48,116)( 49,121)( 50,122)( 51,123)( 52,124)( 53,129)( 54,130)( 55,131)
( 56,132)( 57,125)( 58,126)( 59,127)( 60,128)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,141)( 66,142)( 67,143)( 68,144)( 69,137)( 70,138)( 71,139)
( 72,140);
s2 := Sym(144)!(  1,  7)(  2,  8)(  3,  5)(  4,  6)(  9, 11)( 10, 12)( 13, 19)
( 14, 20)( 15, 17)( 16, 18)( 21, 23)( 22, 24)( 25, 31)( 26, 32)( 27, 29)
( 28, 30)( 33, 35)( 34, 36)( 37, 43)( 38, 44)( 39, 41)( 40, 42)( 45, 47)
( 46, 48)( 49, 55)( 50, 56)( 51, 53)( 52, 54)( 57, 59)( 58, 60)( 61, 67)
( 62, 68)( 63, 65)( 64, 66)( 69, 71)( 70, 72)( 73, 79)( 74, 80)( 75, 77)
( 76, 78)( 81, 83)( 82, 84)( 85, 91)( 86, 92)( 87, 89)( 88, 90)( 93, 95)
( 94, 96)( 97,103)( 98,104)( 99,101)(100,102)(105,107)(106,108)(109,115)
(110,116)(111,113)(112,114)(117,119)(118,120)(121,127)(122,128)(123,125)
(124,126)(129,131)(130,132)(133,139)(134,140)(135,137)(136,138)(141,143)
(142,144);
s3 := 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);
s4 := 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, 85)
( 74, 88)( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)
( 82, 96)( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)
(111,123)(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)
(119,131)(120,130)(134,136)(138,140)(142,144);
poly := sub<Sym(144)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
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