Polytope of Type {6,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157559)
Rank : 4
Schlafli Type : {6,6,12}
Number of vertices, edges, etc : 6, 24, 48, 16
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 : {6,6,6}*576a
   3-fold quotients : {2,6,12}*384a
   4-fold quotients : {6,6,3}*288
   6-fold quotients : {2,6,6}*192
   12-fold quotients : {6,2,4}*96, {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {3,2,4}*48, {2,3,3}*48, {6,2,2}*48
   36-fold quotients : {2,2,4}*32
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope