Polytope of Type {92,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope