Polytope of Type {22,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6}*1452
Also Known As : {22,6}₃. if this polytope has another name.
Group : SmallGroup(1452,22)
Rank : 3
Schlafli Type : {22,6}
Number of vertices, edges, etc : 121, 363, 33
Order of s₀s₁s₂ : 3
Order of s₀s₁s₂s₁ : 22
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
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 := (  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, 35)(  3, 58)(  4, 81)(  5,104)(  7, 29)(  8, 52)(  9, 75)
( 10, 98)( 11,121)( 13, 24)( 14, 47)( 15, 70)( 16, 93)( 17,116)( 19, 41)
( 20, 64)( 21, 87)( 22,110)( 23,111)( 25, 36)( 26, 59)( 27, 82)( 28,105)
( 31, 53)( 32, 76)( 33, 99)( 34,100)( 37, 48)( 38, 71)( 39, 94)( 40,117)
( 43, 65)( 44, 88)( 45, 89)( 46,112)( 49, 60)( 50, 83)( 51,106)( 55, 77)
( 56, 78)( 57,101)( 61, 72)( 62, 95)( 63,118)( 68, 90)( 69,113)( 73, 84)
( 74,107)( 80,102)( 85, 96)( 86,119)( 92,114)( 97,108)(109,120);;
s2 := (  2,104)(  3, 86)(  4, 57)(  5, 39)(  6, 21)(  7,113)(  8, 95)(  9, 77)
( 10, 48)( 11, 30)( 12, 80)( 13, 62)( 14, 44)( 16,118)( 17, 89)( 18, 71)
( 19, 53)( 20, 24)( 22,109)( 23, 38)( 25,112)( 26, 94)( 27, 76)( 28, 47)
( 31,103)( 32, 85)( 33, 56)( 34,117)( 35, 99)( 36, 70)( 37, 52)( 40,108)
( 41, 79)( 42, 61)( 45, 75)( 49,102)( 50, 84)( 51, 66)( 54,111)( 55, 93)
( 58,107)( 59, 78)( 63,116)( 64, 98)( 65, 69)( 67,101)( 68, 83)( 72,121)
( 73, 92)( 81,115)( 82, 97)( 87,106)( 90,120)( 96,100)(110,114);;
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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
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, 35)(  3, 58)(  4, 81)(  5,104)(  7, 29)(  8, 52)
(  9, 75)( 10, 98)( 11,121)( 13, 24)( 14, 47)( 15, 70)( 16, 93)( 17,116)
( 19, 41)( 20, 64)( 21, 87)( 22,110)( 23,111)( 25, 36)( 26, 59)( 27, 82)
( 28,105)( 31, 53)( 32, 76)( 33, 99)( 34,100)( 37, 48)( 38, 71)( 39, 94)
( 40,117)( 43, 65)( 44, 88)( 45, 89)( 46,112)( 49, 60)( 50, 83)( 51,106)
( 55, 77)( 56, 78)( 57,101)( 61, 72)( 62, 95)( 63,118)( 68, 90)( 69,113)
( 73, 84)( 74,107)( 80,102)( 85, 96)( 86,119)( 92,114)( 97,108)(109,120);
s2 := Sym(121)!(  2,104)(  3, 86)(  4, 57)(  5, 39)(  6, 21)(  7,113)(  8, 95)
(  9, 77)( 10, 48)( 11, 30)( 12, 80)( 13, 62)( 14, 44)( 16,118)( 17, 89)
( 18, 71)( 19, 53)( 20, 24)( 22,109)( 23, 38)( 25,112)( 26, 94)( 27, 76)
( 28, 47)( 31,103)( 32, 85)( 33, 56)( 34,117)( 35, 99)( 36, 70)( 37, 52)
( 40,108)( 41, 79)( 42, 61)( 45, 75)( 49,102)( 50, 84)( 51, 66)( 54,111)
( 55, 93)( 58,107)( 59, 78)( 63,116)( 64, 98)( 65, 69)( 67,101)( 68, 83)
( 72,121)( 73, 92)( 81,115)( 82, 97)( 87,106)( 90,120)( 96,100)(110,114);
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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;

References : None.
to this polytope