Polytope of Type {14,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,14}*392a
Also Known As : {14,14|2}. if this polytope has another name.
Group : SmallGroup(392,41)
Rank : 3
Schlafli Type : {14,14}
Number of vertices, edges, etc : 14, 98, 14
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {14,14,2} of size 784
   {14,14,4} of size 1568
Vertex Figure Of :
   {2,14,14} of size 784
   {4,14,14} of size 1568
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,14}*56, {14,2}*56
   14-fold quotients : {2,7}*28, {7,2}*28
   49-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,28}*784a, {28,14}*784a
   3-fold covers : {14,42}*1176b, {42,14}*1176b
   4-fold covers : {14,56}*1568a, {56,14}*1568a, {28,28}*1568a
   5-fold covers : {14,70}*1960b, {70,14}*1960b
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)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,50)( 9,51)(10,52)
(11,53)(12,54)(13,55)(14,56)(15,92)(16,93)(17,94)(18,95)(19,96)(20,97)(21,98)
(22,85)(23,86)(24,87)(25,88)(26,89)(27,90)(28,91)(29,78)(30,79)(31,80)(32,81)
(33,82)(34,83)(35,84)(36,71)(37,72)(38,73)(39,74)(40,75)(41,76)(42,77)(43,64)
(44,65)(45,66)(46,67)(47,68)(48,69)(49,70);;
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*s1*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, 
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)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,50)( 9,51)
(10,52)(11,53)(12,54)(13,55)(14,56)(15,92)(16,93)(17,94)(18,95)(19,96)(20,97)
(21,98)(22,85)(23,86)(24,87)(25,88)(26,89)(27,90)(28,91)(29,78)(30,79)(31,80)
(32,81)(33,82)(34,83)(35,84)(36,71)(37,72)(38,73)(39,74)(40,75)(41,76)(42,77)
(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70);
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*s1*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, 
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 : None.
to this polytope