Polytope of Type {2,22,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,4}*1936
if this polytope has a name.
Group : SmallGroup(1936,161)
Rank : 4
Schlafli Type : {2,22,4}
Number of vertices, edges, etc : 2, 121, 242, 22
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   No Regular Quotients.
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)( 14,113)( 15,123)( 16,122)
( 17,121)( 18,120)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)( 24,114)
( 25,102)( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)( 32,106)
( 33,105)( 34,104)( 35,103)( 36, 91)( 37,101)( 38,100)( 39, 99)( 40, 98)
( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 80)( 48, 90)
( 49, 89)( 50, 88)( 51, 87)( 52, 86)( 53, 85)( 54, 84)( 55, 83)( 56, 82)
( 57, 81)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)
( 65, 73)( 66, 72)( 67, 71)( 68, 70);;
s2 := (  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)( 10, 21)
( 11, 22)( 12, 23)( 13, 24)( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)
( 30,118)( 31,119)( 32,120)( 33,121)( 34,122)( 35,123)( 36,102)( 37,103)
( 38,104)( 39,105)( 40,106)( 41,107)( 42,108)( 43,109)( 44,110)( 45,111)
( 46,112)( 47, 91)( 48, 92)( 49, 93)( 50, 94)( 51, 95)( 52, 96)( 53, 97)
( 54, 98)( 55, 99)( 56,100)( 57,101)( 58, 80)( 59, 81)( 60, 82)( 61, 83)
( 62, 84)( 63, 85)( 64, 86)( 65, 87)( 66, 88)( 67, 89)( 68, 90);;
s3 := (  4, 14)(  5, 25)(  6, 36)(  7, 47)(  8, 58)(  9, 69)( 10, 80)( 11, 91)
( 12,102)( 13,113)( 16, 26)( 17, 37)( 18, 48)( 19, 59)( 20, 70)( 21, 81)
( 22, 92)( 23,103)( 24,114)( 28, 38)( 29, 49)( 30, 60)( 31, 71)( 32, 82)
( 33, 93)( 34,104)( 35,115)( 40, 50)( 41, 61)( 42, 72)( 43, 83)( 44, 94)
( 45,105)( 46,116)( 52, 62)( 53, 73)( 54, 84)( 55, 95)( 56,106)( 57,117)
( 64, 74)( 65, 85)( 66, 96)( 67,107)( 68,118)( 76, 86)( 77, 97)( 78,108)
( 79,119)( 88, 98)( 89,109)( 90,120)(100,110)(101,121)(112,122);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*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*s1*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*s3*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(123)!(1,2);
s1 := Sym(123)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 14,113)( 15,123)
( 16,122)( 17,121)( 18,120)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)
( 24,114)( 25,102)( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)
( 32,106)( 33,105)( 34,104)( 35,103)( 36, 91)( 37,101)( 38,100)( 39, 99)
( 40, 98)( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 80)
( 48, 90)( 49, 89)( 50, 88)( 51, 87)( 52, 86)( 53, 85)( 54, 84)( 55, 83)
( 56, 82)( 57, 81)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)
( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70);
s2 := Sym(123)!(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)
( 10, 21)( 11, 22)( 12, 23)( 13, 24)( 25,113)( 26,114)( 27,115)( 28,116)
( 29,117)( 30,118)( 31,119)( 32,120)( 33,121)( 34,122)( 35,123)( 36,102)
( 37,103)( 38,104)( 39,105)( 40,106)( 41,107)( 42,108)( 43,109)( 44,110)
( 45,111)( 46,112)( 47, 91)( 48, 92)( 49, 93)( 50, 94)( 51, 95)( 52, 96)
( 53, 97)( 54, 98)( 55, 99)( 56,100)( 57,101)( 58, 80)( 59, 81)( 60, 82)
( 61, 83)( 62, 84)( 63, 85)( 64, 86)( 65, 87)( 66, 88)( 67, 89)( 68, 90);
s3 := Sym(123)!(  4, 14)(  5, 25)(  6, 36)(  7, 47)(  8, 58)(  9, 69)( 10, 80)
( 11, 91)( 12,102)( 13,113)( 16, 26)( 17, 37)( 18, 48)( 19, 59)( 20, 70)
( 21, 81)( 22, 92)( 23,103)( 24,114)( 28, 38)( 29, 49)( 30, 60)( 31, 71)
( 32, 82)( 33, 93)( 34,104)( 35,115)( 40, 50)( 41, 61)( 42, 72)( 43, 83)
( 44, 94)( 45,105)( 46,116)( 52, 62)( 53, 73)( 54, 84)( 55, 95)( 56,106)
( 57,117)( 64, 74)( 65, 85)( 66, 96)( 67,107)( 68,118)( 76, 86)( 77, 97)
( 78,108)( 79,119)( 88, 98)( 89,109)( 90,120)(100,110)(101,121)(112,122);
poly := sub<Sym(123)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*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*s1*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*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope