Polytope of Type {7,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,14}*196
if this polytope has a name.
Group : SmallGroup(196,9)
Rank : 3
Schlafli Type : {7,14}
Number of vertices, edges, etc : 7, 49, 14
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,14,2} of size 392
   {7,14,4} of size 784
   {7,14,6} of size 1176
   {7,14,7} of size 1372
   {7,14,8} of size 1568
   {7,14,10} of size 1960
Vertex Figure Of :
   {2,7,14} of size 392
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {7,2}*28
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,14}*392c
   3-fold covers : {21,14}*588
   4-fold covers : {28,14}*784b, {14,28}*784c
   5-fold covers : {35,14}*980
   6-fold covers : {14,42}*1176a, {42,14}*1176c
   7-fold covers : {49,14}*1372, {7,14}*1372
   8-fold covers : {56,14}*1568b, {28,28}*1568c, {14,56}*1568c
   9-fold covers : {63,14}*1764, {21,42}*1764
   10-fold covers : {14,70}*1960a, {70,14}*1960c
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);;
s1 := ( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,44)(16,43)(17,49)
(18,48)(19,47)(20,46)(21,45)(22,37)(23,36)(24,42)(25,41)(26,40)(27,39)(28,38)
(29,30)(31,35)(32,34);;
s2 := ( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)(17,38)
(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)
(28,35);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(49)!( 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);
s1 := Sym(49)!( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,44)(16,43)
(17,49)(18,48)(19,47)(20,46)(21,45)(22,37)(23,36)(24,42)(25,41)(26,40)(27,39)
(28,38)(29,30)(31,35)(32,34);
s2 := Sym(49)!( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)
(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)
(28,35);
poly := sub<Sym(49)|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 >;

References : None.
to this polytope