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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,22,11}*1936
if this polytope has a name.
Group : SmallGroup(1936,164)
Rank : 5
Schlafli Type : {2,2,22,11}
Number of vertices, edges, etc : 2, 2, 22, 121, 11
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 : {2,2,2,11}*176
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope