Polytope of Type {4,12,6}

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

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

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, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 >;

References : None.
to this polytope