Polytope of Type {14,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,6}*588
Also Known As : {14,6}₃. if this polytope has another name.
Group : SmallGroup(588,35)
Rank : 3
Schlafli Type : {14,6}
Number of vertices, edges, etc : 49, 147, 21
Order of s₀s₁s₂ : 3
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {14,6,2} of size 1176
Vertex Figure Of :
   {2,14,6} of size 1176
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,6}*1176b
   3-fold covers : {14,18}*1764, {42,6}*1764
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)( 3,44)( 4,37)( 5,30)( 6,23)( 7,16)(10,43)(11,36)(12,29)(13,22)
(14,15)(17,49)(18,42)(19,35)(20,28)(24,48)(25,41)(26,34)(31,47)(32,40)
(38,46);;
s2 := ( 2,29)( 3, 8)( 4,36)( 5,15)( 6,43)( 7,22)( 9,31)(11,38)(12,17)(13,45)
(14,24)(16,33)(18,40)(20,47)(21,26)(23,35)(25,42)(27,49)(32,37)(34,44)
(41,46);;
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*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
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)( 3,44)( 4,37)( 5,30)( 6,23)( 7,16)(10,43)(11,36)(12,29)
(13,22)(14,15)(17,49)(18,42)(19,35)(20,28)(24,48)(25,41)(26,34)(31,47)(32,40)
(38,46);
s2 := Sym(49)!( 2,29)( 3, 8)( 4,36)( 5,15)( 6,43)( 7,22)( 9,31)(11,38)(12,17)
(13,45)(14,24)(16,33)(18,40)(20,47)(21,26)(23,35)(25,42)(27,49)(32,37)(34,44)
(41,46);
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*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;

References : None.
to this polytope