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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,14,4}*1120
if this polytope has a name.
Group : SmallGroup(1120,998)
Rank : 5
Schlafli Type : {5,2,14,4}
Number of vertices, edges, etc : 5, 5, 14, 28, 4
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 : {5,2,14,2}*560
   4-fold quotients : {5,2,7,2}*280
   7-fold quotients : {5,2,2,4}*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 := ( 8, 9)(11,12)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)
(30,31)(32,33);;
s3 := ( 6, 8)( 7,16)( 9,13)(10,11)(12,24)(14,20)(15,22)(17,18)(19,30)(23,28)
(25,26)(27,31)(29,32);;
s4 := ( 6, 7)( 8,11)( 9,12)(10,15)(13,18)(14,19)(16,22)(17,23)(20,26)(21,27)
(24,28)(25,29)(30,32)(31,33);;
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope