Polytope of Type {3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6}*1452
Also Known As : {3,6}_(11,0), {3,6}₂₂. if this polytope has another name.
Group : SmallGroup(1452,22)
Rank : 3
Schlafli Type : {3,6}
Number of vertices, edges, etc : 121, 363, 242
Order of s₀s₁s₂ : 22
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Toroidal
   Locally Spherical
   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, 24)(  3, 47)(  4, 70)(  5, 93)(  6,116)(  7, 18)(  8, 41)(  9, 64)
( 10, 87)( 11,110)( 12,111)( 14, 36)( 15, 59)( 16, 82)( 17,105)( 19, 30)
( 20, 53)( 21, 76)( 22, 99)( 23,100)( 26, 48)( 27, 71)( 28, 94)( 29,117)
( 31, 42)( 32, 65)( 33, 88)( 34, 89)( 35,112)( 38, 60)( 39, 83)( 40,106)
( 43, 54)( 44, 77)( 45, 78)( 46,101)( 50, 72)( 51, 95)( 52,118)( 55, 66)
( 56, 67)( 57, 90)( 58,113)( 62, 84)( 63,107)( 68, 79)( 69,102)( 74, 96)
( 75,119)( 80, 91)( 81,114)( 86,108)( 92,103)( 98,120)(104,115);;
s2 := (  1, 35)(  2, 17)(  3,120)(  4, 91)(  5, 73)(  6, 55)(  7, 26)(  9,100)
( 10, 82)( 11, 64)( 12,114)( 13, 96)( 14, 67)( 15, 49)( 16, 31)( 18,105)
( 19, 87)( 20, 58)( 21, 40)( 23, 72)( 24, 54)( 27,110)( 28, 81)( 29, 63)
( 30, 34)( 32,119)( 33, 90)( 36,104)( 37, 86)( 38, 57)( 41,113)( 42, 95)
( 43, 77)( 44, 48)( 45,109)( 46, 80)( 47, 62)( 50,118)( 51, 89)( 52, 71)
( 59,112)( 60, 94)( 61, 76)( 65,103)( 66, 85)( 68,117)( 69, 99)( 74,108)
( 75, 79)( 78, 93)( 83,102)( 88,111)( 92,107)( 97,116)(106,121);;
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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
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, 24)(  3, 47)(  4, 70)(  5, 93)(  6,116)(  7, 18)(  8, 41)
(  9, 64)( 10, 87)( 11,110)( 12,111)( 14, 36)( 15, 59)( 16, 82)( 17,105)
( 19, 30)( 20, 53)( 21, 76)( 22, 99)( 23,100)( 26, 48)( 27, 71)( 28, 94)
( 29,117)( 31, 42)( 32, 65)( 33, 88)( 34, 89)( 35,112)( 38, 60)( 39, 83)
( 40,106)( 43, 54)( 44, 77)( 45, 78)( 46,101)( 50, 72)( 51, 95)( 52,118)
( 55, 66)( 56, 67)( 57, 90)( 58,113)( 62, 84)( 63,107)( 68, 79)( 69,102)
( 74, 96)( 75,119)( 80, 91)( 81,114)( 86,108)( 92,103)( 98,120)(104,115);
s2 := Sym(121)!(  1, 35)(  2, 17)(  3,120)(  4, 91)(  5, 73)(  6, 55)(  7, 26)
(  9,100)( 10, 82)( 11, 64)( 12,114)( 13, 96)( 14, 67)( 15, 49)( 16, 31)
( 18,105)( 19, 87)( 20, 58)( 21, 40)( 23, 72)( 24, 54)( 27,110)( 28, 81)
( 29, 63)( 30, 34)( 32,119)( 33, 90)( 36,104)( 37, 86)( 38, 57)( 41,113)
( 42, 95)( 43, 77)( 44, 48)( 45,109)( 46, 80)( 47, 62)( 50,118)( 51, 89)
( 52, 71)( 59,112)( 60, 94)( 61, 76)( 65,103)( 66, 85)( 68,117)( 69, 99)
( 74,108)( 75, 79)( 78, 93)( 83,102)( 88,111)( 92,107)( 97,116)(106,121);
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*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope