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

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

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

Permutation Representation (Magma) :

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

to this polytope