Polytope of Type {14,8} with group SmallGroup(1568,917)

Overview

Group: SmallGroup(1568,917)
Rank: 3
Schläfli Type: {14,8}
Vertices, edges, …: 98, 392, 56
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 14
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{14,8}*784a

49-fold

{2,8}*32

98-fold

{2,4}*16

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=<(s0*s1*s2*s1)^2> of order 7

8 facets

8 of {14}*28

14 vertex figures

14 of {8}*16

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

20 facets

14 of {2}*4
6 of {14}*28

14 vertex figures

14 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.