Polytope of Type {3,2,7,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,7,14}*1176
if this polytope has a name.
Group : SmallGroup(1176,237)
Rank : 5
Schlafli Type : {3,2,7,14}
Number of vertices, edges, etc : 3, 3, 7, 49, 14
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   7-fold quotients : {3,2,7,2}*168
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5,10)( 6, 9)( 7, 8)(11,46)(12,52)(13,51)(14,50)(15,49)(16,48)(17,47)
(18,39)(19,45)(20,44)(21,43)(22,42)(23,41)(24,40)(25,32)(26,38)(27,37)(28,36)
(29,35)(30,34)(31,33);;
s3 := ( 4,12)( 5,11)( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(18,47)(19,46)(20,52)
(21,51)(22,50)(23,49)(24,48)(25,40)(26,39)(27,45)(28,44)(29,43)(30,42)(31,41)
(32,33)(34,38)(35,37);;
s4 := (11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,39)(19,40)(20,41)
(21,42)(22,43)(23,44)(24,45)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)
(31,38);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!(2,3);
s1 := Sym(52)!(1,2);
s2 := Sym(52)!( 5,10)( 6, 9)( 7, 8)(11,46)(12,52)(13,51)(14,50)(15,49)(16,48)
(17,47)(18,39)(19,45)(20,44)(21,43)(22,42)(23,41)(24,40)(25,32)(26,38)(27,37)
(28,36)(29,35)(30,34)(31,33);
s3 := Sym(52)!( 4,12)( 5,11)( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(18,47)(19,46)
(20,52)(21,51)(22,50)(23,49)(24,48)(25,40)(26,39)(27,45)(28,44)(29,43)(30,42)
(31,41)(32,33)(34,38)(35,37);
s4 := Sym(52)!(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,39)(19,40)
(20,41)(21,42)(22,43)(23,44)(24,45)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)
(31,38);
poly := sub<Sym(52)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope