Polytope of Type {2,22,12}

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

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

to this polytope