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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,11,22}*1936
if this polytope has a name.
Group : SmallGroup(1936,164)
Rank : 5
Schlafli Type : {2,2,11,22}
Number of vertices, edges, etc : 2, 2, 11, 121, 22
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 := (3,4);;
s2 := (  6, 15)(  7, 14)(  8, 13)(  9, 12)( 10, 11)( 16,115)( 17,125)( 18,124)
( 19,123)( 20,122)( 21,121)( 22,120)( 23,119)( 24,118)( 25,117)( 26,116)
( 27,104)( 28,114)( 29,113)( 30,112)( 31,111)( 32,110)( 33,109)( 34,108)
( 35,107)( 36,106)( 37,105)( 38, 93)( 39,103)( 40,102)( 41,101)( 42,100)
( 43, 99)( 44, 98)( 45, 97)( 46, 96)( 47, 95)( 48, 94)( 49, 82)( 50, 92)
( 51, 91)( 52, 90)( 53, 89)( 54, 88)( 55, 87)( 56, 86)( 57, 85)( 58, 84)
( 59, 83)( 60, 71)( 61, 81)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 76)
( 67, 75)( 68, 74)( 69, 73)( 70, 72);;
s3 := (  5, 17)(  6, 16)(  7, 26)(  8, 25)(  9, 24)( 10, 23)( 11, 22)( 12, 21)
( 13, 20)( 14, 19)( 15, 18)( 27,116)( 28,115)( 29,125)( 30,124)( 31,123)
( 32,122)( 33,121)( 34,120)( 35,119)( 36,118)( 37,117)( 38,105)( 39,104)
( 40,114)( 41,113)( 42,112)( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)
( 48,106)( 49, 94)( 50, 93)( 51,103)( 52,102)( 53,101)( 54,100)( 55, 99)
( 56, 98)( 57, 97)( 58, 96)( 59, 95)( 60, 83)( 61, 82)( 62, 92)( 63, 91)
( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 72)
( 73, 81)( 74, 80)( 75, 79)( 76, 78);;
s4 := (  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);;
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*s4*s3*s4*s2*s3*s4*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(125)!(1,2);
s1 := Sym(125)!(3,4);
s2 := Sym(125)!(  6, 15)(  7, 14)(  8, 13)(  9, 12)( 10, 11)( 16,115)( 17,125)
( 18,124)( 19,123)( 20,122)( 21,121)( 22,120)( 23,119)( 24,118)( 25,117)
( 26,116)( 27,104)( 28,114)( 29,113)( 30,112)( 31,111)( 32,110)( 33,109)
( 34,108)( 35,107)( 36,106)( 37,105)( 38, 93)( 39,103)( 40,102)( 41,101)
( 42,100)( 43, 99)( 44, 98)( 45, 97)( 46, 96)( 47, 95)( 48, 94)( 49, 82)
( 50, 92)( 51, 91)( 52, 90)( 53, 89)( 54, 88)( 55, 87)( 56, 86)( 57, 85)
( 58, 84)( 59, 83)( 60, 71)( 61, 81)( 62, 80)( 63, 79)( 64, 78)( 65, 77)
( 66, 76)( 67, 75)( 68, 74)( 69, 73)( 70, 72);
s3 := Sym(125)!(  5, 17)(  6, 16)(  7, 26)(  8, 25)(  9, 24)( 10, 23)( 11, 22)
( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 27,116)( 28,115)( 29,125)( 30,124)
( 31,123)( 32,122)( 33,121)( 34,120)( 35,119)( 36,118)( 37,117)( 38,105)
( 39,104)( 40,114)( 41,113)( 42,112)( 43,111)( 44,110)( 45,109)( 46,108)
( 47,107)( 48,106)( 49, 94)( 50, 93)( 51,103)( 52,102)( 53,101)( 54,100)
( 55, 99)( 56, 98)( 57, 97)( 58, 96)( 59, 95)( 60, 83)( 61, 82)( 62, 92)
( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)
( 71, 72)( 73, 81)( 74, 80)( 75, 79)( 76, 78);
s4 := 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);
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*s4*s3*s4*s2*s3*s4*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