Polytope of Type {14,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,8}*784b
if this polytope has a name.
Group : SmallGroup(784,161)
Rank : 3
Schlafli Type : {14,8}
Number of vertices, edges, etc : 49, 196, 28
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 :
   {14,8,2} of size 1568
Vertex Figure Of :
   {2,14,8} of size 1568
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,8}*1568b
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, 2)( 3, 7)( 4, 6)( 8,14)( 9,13)(10,12)(15,19)(16,18)(20,21)(22,24)
(25,28)(26,27)(30,35)(31,34)(32,33)(36,41)(37,40)(38,39)(43,46)(44,45)
(47,49);;
s2 := ( 2,46)( 3,42)( 4,31)( 5,27)( 6,16)( 7,12)( 8,30)( 9,26)(10,15)(13,45)
(14,41)(17,44)(18,40)(19,29)(20,25)(22,39)(23,35)(28,43)(32,49)(33,38)
(36,48);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
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, 2)( 3, 7)( 4, 6)( 8,14)( 9,13)(10,12)(15,19)(16,18)(20,21)
(22,24)(25,28)(26,27)(30,35)(31,34)(32,33)(36,41)(37,40)(38,39)(43,46)(44,45)
(47,49);
s2 := Sym(49)!( 2,46)( 3,42)( 4,31)( 5,27)( 6,16)( 7,12)( 8,30)( 9,26)(10,15)
(13,45)(14,41)(17,44)(18,40)(19,29)(20,25)(22,39)(23,35)(28,43)(32,49)(33,38)
(36,48);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 >;

References : None.
to this polytope