Polytope of Type {22,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,4}*968
if this polytope has a name.
Group : SmallGroup(968,36)
Rank : 3
Schlafli Type : {22,4}
Number of vertices, edges, etc : 121, 242, 22
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 22
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {22,4,2} of size 1936
Vertex Figure Of :
   {2,22,4} of size 1936
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {22,4}*1936
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope