Polytope of Type {2,22,11,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,11,2}*1936
if this polytope has a name.
Group : SmallGroup(1936,164)
Rank : 5
Schlafli Type : {2,22,11,2}
Number of vertices, edges, etc : 2, 22, 121, 11, 2
Order of s₀s₁s₂s₃s₄ : 22
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   11-fold quotients : {2,2,11,2}*176
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);;
s2 := (  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14,114)( 15,113)( 16,123)
( 17,122)( 18,121)( 19,120)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)
( 25,103)( 26,102)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)
( 33,106)( 34,105)( 35,104)( 36, 92)( 37, 91)( 38,101)( 39,100)( 40, 99)
( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 81)( 48, 80)
( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)
( 57, 82)( 58, 70)( 59, 69)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71);;
s3 := (  3, 14)(  4, 24)(  5, 23)(  6, 22)(  7, 21)(  8, 20)(  9, 19)( 10, 18)
( 11, 17)( 12, 16)( 13, 15)( 25,113)( 26,123)( 27,122)( 28,121)( 29,120)
( 30,119)( 31,118)( 32,117)( 33,116)( 34,115)( 35,114)( 36,102)( 37,112)
( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43,106)( 44,105)( 45,104)
( 46,103)( 47, 91)( 48,101)( 49,100)( 50, 99)( 51, 98)( 52, 97)( 53, 96)
( 54, 95)( 55, 94)( 56, 93)( 57, 92)( 58, 80)( 59, 90)( 60, 89)( 61, 88)
( 62, 87)( 63, 86)( 64, 85)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75);;
s4 := (124,125);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(125)!(1,2);
s1 := Sym(125)!(  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);
s2 := Sym(125)!(  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14,114)( 15,113)
( 16,123)( 17,122)( 18,121)( 19,120)( 20,119)( 21,118)( 22,117)( 23,116)
( 24,115)( 25,103)( 26,102)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)
( 32,107)( 33,106)( 34,105)( 35,104)( 36, 92)( 37, 91)( 38,101)( 39,100)
( 40, 99)( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 81)
( 48, 80)( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)
( 56, 83)( 57, 82)( 58, 70)( 59, 69)( 60, 79)( 61, 78)( 62, 77)( 63, 76)
( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71);
s3 := Sym(125)!(  3, 14)(  4, 24)(  5, 23)(  6, 22)(  7, 21)(  8, 20)(  9, 19)
( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 25,113)( 26,123)( 27,122)( 28,121)
( 29,120)( 30,119)( 31,118)( 32,117)( 33,116)( 34,115)( 35,114)( 36,102)
( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43,106)( 44,105)
( 45,104)( 46,103)( 47, 91)( 48,101)( 49,100)( 50, 99)( 51, 98)( 52, 97)
( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 92)( 58, 80)( 59, 90)( 60, 89)
( 61, 88)( 62, 87)( 63, 86)( 64, 85)( 65, 84)( 66, 83)( 67, 82)( 68, 81)
( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75);
s4 := Sym(125)!(124,125);
poly := sub<Sym(125)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s3*s1*s2*s1*s2*s3*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 >;

to this polytope