Polytope of Type {8,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,14}*784a
if this polytope has a name.
Group : SmallGroup(784,161)
Rank : 3
Schlafli Type : {8,14}
Number of vertices, edges, etc : 28, 196, 49
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,14,2} of size 1568
Vertex Figure Of :
   {2,8,14} of size 1568
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,14}*1568b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope