Polytope of Type {6,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,99266)
Rank : 4
Schlafli Type : {6,12,4}
Number of vertices, edges, etc : 6, 72, 48, 8
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 : {6,12,4}*576a
   3-fold quotients : {2,12,4}*384a, {6,4,4}*384a
   4-fold quotients : {6,12,2}*288a, {6,6,4}*288a
   6-fold quotients : {2,12,4}*192a, {6,4,4}*192
   8-fold quotients : {6,6,2}*144a
   9-fold quotients : {2,4,4}*128
   12-fold quotients : {2,12,2}*96, {2,6,4}*96a, {6,2,4}*96, {6,4,2}*96a
   18-fold quotients : {2,4,4}*64
   24-fold quotients : {3,2,4}*48, {2,6,2}*48, {6,2,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {2,3,2}*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 := (  1, 37)(  2, 42)(  3, 44)(  4, 40)(  5, 45)(  6, 38)(  7, 43)(  8, 39)
(  9, 41)( 10, 46)( 11, 51)( 12, 53)( 13, 49)( 14, 54)( 15, 47)( 16, 52)
( 17, 48)( 18, 50)( 19, 55)( 20, 60)( 21, 62)( 22, 58)( 23, 63)( 24, 56)
( 25, 61)( 26, 57)( 27, 59)( 28, 64)( 29, 69)( 30, 71)( 31, 67)( 32, 72)
( 33, 65)( 34, 70)( 35, 66)( 36, 68)( 73,109)( 74,114)( 75,116)( 76,112)
( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)
( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,127)( 92,132)
( 93,134)( 94,130)( 95,135)( 96,128)( 97,133)( 98,129)( 99,131)(100,136)
(101,141)(102,143)(103,139)(104,144)(105,137)(106,142)(107,138)(108,140);;
s1 := (  1, 74)(  2, 73)(  3, 75)(  4, 80)(  5, 79)(  6, 81)(  7, 77)(  8, 76)
(  9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)
( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)( 24, 99)
( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)( 32,106)
( 33,108)( 34,104)( 35,103)( 36,105)( 37,110)( 38,109)( 39,111)( 40,116)
( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)( 48,120)
( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)( 56,127)
( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)
( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141);;
s2 := (  1, 37)(  2, 44)(  3, 42)(  4, 43)(  5, 41)(  6, 39)(  7, 40)(  8, 38)
(  9, 45)( 10, 46)( 11, 53)( 12, 51)( 13, 52)( 14, 50)( 15, 48)( 16, 49)
( 17, 47)( 18, 54)( 19, 55)( 20, 62)( 21, 60)( 22, 61)( 23, 59)( 24, 57)
( 25, 58)( 26, 56)( 27, 63)( 28, 64)( 29, 71)( 30, 69)( 31, 70)( 32, 68)
( 33, 66)( 34, 67)( 35, 65)( 36, 72)( 73,127)( 74,134)( 75,132)( 76,133)
( 77,131)( 78,129)( 79,130)( 80,128)( 81,135)( 82,136)( 83,143)( 84,141)
( 85,142)( 86,140)( 87,138)( 88,139)( 89,137)( 90,144)( 91,109)( 92,116)
( 93,114)( 94,115)( 95,113)( 96,111)( 97,112)( 98,110)( 99,117)(100,118)
(101,125)(102,123)(103,124)(104,122)(105,120)(106,121)(107,119)(108,126);;
s3 := ( 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);;
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*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope