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
Self-Petrie

Quotients maximal quotients in bold

2-fold

{14,7}*196

7-fold

{2,14}*56

14-fold

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

Permutation Representation (Magma)

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

References