Polytope of Type {69,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {69,6}*1104
if this polytope has a name.
Group : SmallGroup(1104,160)
Rank : 3
Schlafli Type : {69,6}
Number of vertices, edges, etc : 92, 276, 8
Order of s₀s₁s₂ : 92
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   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) :
   12-fold quotients : {23,2}*92
   23-fold quotients : {3,6}*48
   46-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,89)( 6,90)( 7,92)( 8,91)( 9,85)(10,86)(11,88)(12,87)(13,81)
(14,82)(15,84)(16,83)(17,77)(18,78)(19,80)(20,79)(21,73)(22,74)(23,76)(24,75)
(25,69)(26,70)(27,72)(28,71)(29,65)(30,66)(31,68)(32,67)(33,61)(34,62)(35,64)
(36,63)(37,57)(38,58)(39,60)(40,59)(41,53)(42,54)(43,56)(44,55)(45,49)(46,50)
(47,52)(48,51);;
s1 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,89)(10,92)(11,91)(12,90)(13,85)(14,88)
(15,87)(16,86)(17,81)(18,84)(19,83)(20,82)(21,77)(22,80)(23,79)(24,78)(25,73)
(26,76)(27,75)(28,74)(29,69)(30,72)(31,71)(32,70)(33,65)(34,68)(35,67)(36,66)
(37,61)(38,64)(39,63)(40,62)(41,57)(42,60)(43,59)(44,58)(45,53)(46,56)(47,55)
(48,54)(50,52);;
s2 := ( 1, 2)( 5, 6)( 9,10)(13,14)(17,18)(21,22)(25,26)(29,30)(33,34)(37,38)
(41,42)(45,46)(49,50)(53,54)(57,58)(61,62)(65,66)(69,70)(73,74)(77,78)(81,82)
(85,86)(89,90);;
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*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(92)!( 3, 4)( 5,89)( 6,90)( 7,92)( 8,91)( 9,85)(10,86)(11,88)(12,87)
(13,81)(14,82)(15,84)(16,83)(17,77)(18,78)(19,80)(20,79)(21,73)(22,74)(23,76)
(24,75)(25,69)(26,70)(27,72)(28,71)(29,65)(30,66)(31,68)(32,67)(33,61)(34,62)
(35,64)(36,63)(37,57)(38,58)(39,60)(40,59)(41,53)(42,54)(43,56)(44,55)(45,49)
(46,50)(47,52)(48,51);
s1 := Sym(92)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,89)(10,92)(11,91)(12,90)(13,85)
(14,88)(15,87)(16,86)(17,81)(18,84)(19,83)(20,82)(21,77)(22,80)(23,79)(24,78)
(25,73)(26,76)(27,75)(28,74)(29,69)(30,72)(31,71)(32,70)(33,65)(34,68)(35,67)
(36,66)(37,61)(38,64)(39,63)(40,62)(41,57)(42,60)(43,59)(44,58)(45,53)(46,56)
(47,55)(48,54)(50,52);
s2 := Sym(92)!( 1, 2)( 5, 6)( 9,10)(13,14)(17,18)(21,22)(25,26)(29,30)(33,34)
(37,38)(41,42)(45,46)(49,50)(53,54)(57,58)(61,62)(65,66)(69,70)(73,74)(77,78)
(81,82)(85,86)(89,90);
poly := sub<Sym(92)|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*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s0*s1*s0*s2*s1*s0 >;

References : None.
to this polytope