Polytope of Type {6,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,22}*1452
Also Known As : {6,22}₃. if this polytope has another name.
Group : SmallGroup(1452,22)
Rank : 3
Schlafli Type : {6,22}
Number of vertices, edges, etc : 33, 363, 121
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, 30)(  3, 48)(  4, 77)(  5, 95)(  6,113)(  7, 21)(  8, 39)(  9, 57)
( 10, 86)( 11,104)( 12, 54)( 13, 72)( 14, 90)( 15,119)( 17, 34)( 18, 63)
( 19, 81)( 20,110)( 22, 25)( 23, 96)( 24,114)( 26, 40)( 27, 58)( 28, 87)
( 29,105)( 32, 49)( 33, 67)( 36, 64)( 37, 82)( 38,100)( 41, 55)( 42, 73)
( 43, 91)( 44,120)( 45, 59)( 46, 88)( 47,106)( 51, 68)( 52, 97)( 53,115)
( 56,101)( 60, 74)( 61, 92)( 62,121)( 66, 83)( 70, 98)( 71,116)( 75, 78)
( 76,107)( 79, 93)( 80,111)( 85,102)( 89,117)( 94,108)(109,112);;
s1 := (  2,110)(  3, 87)(  4, 64)(  5, 41)(  6, 18)(  7,116)(  8, 93)(  9, 70)
( 10, 47)( 11, 24)( 13,121)( 14, 98)( 15, 75)( 16, 52)( 17, 29)( 19,104)
( 20, 81)( 21, 58)( 22, 35)( 25,109)( 26, 86)( 27, 63)( 28, 40)( 30,115)
( 31, 92)( 32, 69)( 33, 46)( 36,120)( 37, 97)( 38, 74)( 39, 51)( 42,103)
( 43, 80)( 44, 57)( 48,108)( 49, 85)( 50, 62)( 53,114)( 54, 91)( 55, 68)
( 59,119)( 60, 96)( 61, 73)( 65,102)( 66, 79)( 71,107)( 72, 84)( 76,113)
( 77, 90)( 82,118)( 83, 95)( 88,101)( 94,106)( 99,112)(105,117);;
s2 := (  1, 35)(  2, 34)(  3, 44)(  4, 43)(  5, 42)(  6, 41)(  7, 40)(  8, 39)
(  9, 38)( 10, 37)( 11, 36)( 12, 24)( 13, 23)( 14, 33)( 15, 32)( 16, 31)
( 17, 30)( 18, 29)( 19, 28)( 20, 27)( 21, 26)( 22, 25)( 45,112)( 46,111)
( 47,121)( 48,120)( 49,119)( 50,118)( 51,117)( 52,116)( 53,115)( 54,114)
( 55,113)( 56,101)( 57,100)( 58,110)( 59,109)( 60,108)( 61,107)( 62,106)
( 63,105)( 64,104)( 65,103)( 66,102)( 67, 90)( 68, 89)( 69, 99)( 70, 98)
( 71, 97)( 72, 96)( 73, 95)( 74, 94)( 75, 93)( 76, 92)( 77, 91)( 78, 79)
( 80, 88)( 81, 87)( 82, 86)( 83, 85);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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