Polytope of Type {3,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,14,2}*1176
if this polytope has a name.
Group : SmallGroup(1176,225)
Rank : 4
Schlafli Type : {3,14,2}
Number of vertices, edges, etc : 21, 147, 98, 2
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   49-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s3 := (50,51);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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(51)!( 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(51)!( 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(51)!( 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);
s3 := Sym(51)!(50,51);
poly := sub<Sym(51)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >;

to this polytope