Polytope of Type {6,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157559)
Rank : 4
Schlafli Type : {6,12,6}
Number of vertices, edges, etc : 6, 48, 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 : {6,6,6}*576a
   3-fold quotients : {2,12,6}*384a
   4-fold quotients : {6,6,3}*288
   6-fold quotients : {2,6,6}*192
   12-fold quotients : {6,4,2}*96a, {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {2,3,3}*48, {6,2,2}*48
   36-fold quotients : {2,4,2}*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)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)( 78,110)
( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)( 86,138)
( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)
( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)
(103,124)(104,123)(105,129)(106,130)(107,132)(108,131);;
s2 := (  1, 85)(  2, 88)(  3, 87)(  4, 86)(  5, 89)(  6, 92)(  7, 91)(  8, 90)
(  9, 93)( 10, 96)( 11, 95)( 12, 94)( 13, 73)( 14, 76)( 15, 75)( 16, 74)
( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 81)( 22, 84)( 23, 83)( 24, 82)
( 25, 97)( 26,100)( 27, 99)( 28, 98)( 29,101)( 30,104)( 31,103)( 32,102)
( 33,105)( 34,108)( 35,107)( 36,106)( 37,121)( 38,124)( 39,123)( 40,122)
( 41,125)( 42,128)( 43,127)( 44,126)( 45,129)( 46,132)( 47,131)( 48,130)
( 49,109)( 50,112)( 51,111)( 52,110)( 53,113)( 54,116)( 55,115)( 56,114)
( 57,117)( 58,120)( 59,119)( 60,118)( 61,133)( 62,136)( 63,135)( 64,134)
( 65,137)( 66,140)( 67,139)( 68,138)( 69,141)( 70,144)( 71,143)( 72,142);;
s3 := (  1,  2)(  5,  6)(  9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)( 17, 30)
( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 38)
( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)( 54, 65)
( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 74)( 77, 78)
( 81, 82)( 85, 98)( 86, 97)( 87, 99)( 88,100)( 89,102)( 90,101)( 91,103)
( 92,104)( 93,106)( 94,105)( 95,107)( 96,108)(109,110)(113,114)(117,118)
(121,134)(122,133)(123,135)(124,136)(125,138)(126,137)(127,139)(128,140)
(129,142)(130,141)(131,143)(132,144);;
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, 
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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)
( 78,110)( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)
( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)
( 94,142)( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)
(102,122)(103,124)(104,123)(105,129)(106,130)(107,132)(108,131);
s2 := Sym(144)!(  1, 85)(  2, 88)(  3, 87)(  4, 86)(  5, 89)(  6, 92)(  7, 91)
(  8, 90)(  9, 93)( 10, 96)( 11, 95)( 12, 94)( 13, 73)( 14, 76)( 15, 75)
( 16, 74)( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 81)( 22, 84)( 23, 83)
( 24, 82)( 25, 97)( 26,100)( 27, 99)( 28, 98)( 29,101)( 30,104)( 31,103)
( 32,102)( 33,105)( 34,108)( 35,107)( 36,106)( 37,121)( 38,124)( 39,123)
( 40,122)( 41,125)( 42,128)( 43,127)( 44,126)( 45,129)( 46,132)( 47,131)
( 48,130)( 49,109)( 50,112)( 51,111)( 52,110)( 53,113)( 54,116)( 55,115)
( 56,114)( 57,117)( 58,120)( 59,119)( 60,118)( 61,133)( 62,136)( 63,135)
( 64,134)( 65,137)( 66,140)( 67,139)( 68,138)( 69,141)( 70,144)( 71,143)
( 72,142);
s3 := Sym(144)!(  1,  2)(  5,  6)(  9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)
( 17, 30)( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)
( 37, 38)( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)
( 54, 65)( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 74)
( 77, 78)( 81, 82)( 85, 98)( 86, 97)( 87, 99)( 88,100)( 89,102)( 90,101)
( 91,103)( 92,104)( 93,106)( 94,105)( 95,107)( 96,108)(109,110)(113,114)
(117,118)(121,134)(122,133)(123,135)(124,136)(125,138)(126,137)(127,139)
(128,140)(129,142)(130,141)(131,143)(132,144);
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, 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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References : None.
to this polytope