Polytope of Type {6,92}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,92}*1104b
if this polytope has a name.
Group : SmallGroup(1104,160)
Rank : 3
Schlafli Type : {6,92}
Number of vertices, edges, etc : 6, 276, 92
Order of s₀s₁s₂ : 69
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   23-fold quotients : {6,4}*48b
   46-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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