Polytope of Type {8,8} with group SmallGroup(1568,917)

Overview

Group: SmallGroup(1568,917)
Rank: 3
Schläfli Type: {8,8}
Vertices, edges, …: 98, 392, 98
Order of s₀s₁s₂: 14
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{8,8}*784b

196-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s0*s1*s2*s1*(s0*(s2*s1)^2)^2> of order 2

49 facets

49 of {8}*16

49 vertex figures

49 of {8}*16

P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 7

14 facets

14 of {8}*16

14 vertex figures

14 of {8}*16

Representations

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*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.