Polytope of Type {8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8}*1568b
if this polytope has a name.
Group : SmallGroup(1568,917)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 98, 392, 98
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 4
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) :
   2-fold quotients : {8,8}*784b
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 8,48)( 9,49)(10,43)(11,44)(12,45)(13,46)(14,47)(15,39)(16,40)(17,41)
(18,42)(19,36)(20,37)(21,38)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,29)
(57,97)(58,98)(59,92)(60,93)(61,94)(62,95)(63,96)(64,88)(65,89)(66,90)(67,91)
(68,85)(69,86)(70,87)(71,79)(72,80)(73,81)(74,82)(75,83)(76,84)(77,78);;
s1 := ( 2,39)( 3,28)( 4,10)( 5,48)( 6,30)( 7,19)( 8,33)( 9,15)(11,42)(12,24)
(14,44)(16,47)(17,29)(20,38)(21,27)(22,41)(25,43)(26,32)(31,37)(34,46)(36,49)
(51,88)(52,77)(53,59)(54,97)(55,79)(56,68)(57,82)(58,64)(60,91)(61,73)(63,93)
(65,96)(66,78)(69,87)(70,76)(71,90)(74,92)(75,81)(80,86)(83,95)(85,98);;
s2 := ( 1,51)( 2,50)( 3,56)( 4,55)( 5,54)( 6,53)( 7,52)( 8,60)( 9,59)(10,58)
(11,57)(12,63)(13,62)(14,61)(15,69)(16,68)(17,67)(18,66)(19,65)(20,64)(21,70)
(22,71)(23,77)(24,76)(25,75)(26,74)(27,73)(28,72)(29,80)(30,79)(31,78)(32,84)
(33,83)(34,82)(35,81)(36,89)(37,88)(38,87)(39,86)(40,85)(41,91)(42,90)(43,98)
(44,97)(45,96)(46,95)(47,94)(48,93)(49,92);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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