Polytope of Type {2,12,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,22}*1056
if this polytope has a name.
Group : SmallGroup(1056,916)
Rank : 4
Schlafli Type : {2,12,22}
Number of vertices, edges, etc : 2, 12, 132, 22
Order of s₀s₁s₂s₃ : 132
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,6,22}*528
   3-fold quotients : {2,4,22}*352
   6-fold quotients : {2,2,22}*176
   11-fold quotients : {2,12,2}*96
   12-fold quotients : {2,2,11}*88
   22-fold quotients : {2,6,2}*48
   33-fold quotients : {2,4,2}*32
   44-fold quotients : {2,3,2}*24
   66-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope