Polytope of Type {14,14} with group SmallGroup(392,41)

Overview

Group: SmallGroup(392,41)
Rank: 3
Schläfli Type: {14,14}
Vertices, edges, …: 14, 98, 14
Order of s₀s₁s₂: 14
Order of s₀s₁s₂s₁: 14
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{7,14}*196

7-fold

{14,2}*56

14-fold

{7,2}*28

49-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References