Polytope of Type {5,2,4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,14}*1120
if this polytope has a name.
Group : SmallGroup(1120,998)
Rank : 5
Schlafli Type : {5,2,4,14}
Number of vertices, edges, etc : 5, 5, 4, 28, 14
Order of s₀s₁s₂s₃s₄ : 140
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) :
   2-fold quotients : {5,2,2,14}*560
   4-fold quotients : {5,2,2,7}*280
   7-fold quotients : {5,2,4,2}*160
   14-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7,10)(11,16)(12,17)(18,24)(19,25)(26,30)(27,31);;
s3 := ( 6, 7)( 8,12)( 9,11)(10,15)(13,19)(14,18)(16,23)(17,22)(20,27)(21,26)
(24,29)(25,28)(30,33)(31,32);;
s4 := ( 6, 8)( 7,11)( 9,13)(10,16)(12,18)(14,20)(15,22)(17,24)(19,26)(23,28)
(25,30)(29,32);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(33)!(2,3)(4,5);
s1 := Sym(33)!(1,2)(3,4);
s2 := Sym(33)!( 7,10)(11,16)(12,17)(18,24)(19,25)(26,30)(27,31);
s3 := Sym(33)!( 6, 7)( 8,12)( 9,11)(10,15)(13,19)(14,18)(16,23)(17,22)(20,27)
(21,26)(24,29)(25,28)(30,33)(31,32);
s4 := Sym(33)!( 6, 8)( 7,11)( 9,13)(10,16)(12,18)(14,20)(15,22)(17,24)(19,26)
(23,28)(25,30)(29,32);
poly := sub<Sym(33)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope