Polytope of Type {6,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,3}*576
if this polytope has a name.
Group : SmallGroup(576,8340)
Rank : 4
Schlafli Type : {6,12,3}
Number of vertices, edges, etc : 6, 48, 24, 4
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,12,3,2} of size 1152
Vertex Figure Of :
   {2,6,12,3} of size 1152
   {3,6,12,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6,3}*288
   3-fold quotients : {2,12,3}*192
   6-fold quotients : {2,6,3}*96
   12-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12,3}*1152, {6,12,6}*1152c
   3-fold covers : {18,12,3}*1728, {6,12,3}*1728
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope