Polytope of Type {3,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,14}*588
Also Known As : {3,14}₆. if this polytope has another name.
Group : SmallGroup(588,35)
Rank : 3
Schlafli Type : {3,14}
Number of vertices, edges, etc : 21, 147, 98
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {3,14,2} of size 1176
Vertex Figure Of :
   {2,3,14} of size 1176
Quotients (Maximal Quotients in Boldface) :
   49-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,14}*1176b
   3-fold covers : {9,14}*1764, {3,42}*1764
Permutation Representation (GAP) :

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