Polytope of Type {2,28,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,2,5}*1120
if this polytope has a name.
Group : SmallGroup(1120,989)
Rank : 5
Schlafli Type : {2,28,2,5}
Number of vertices, edges, etc : 2, 28, 28, 5, 5
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 : {2,14,2,5}*560
   4-fold quotients : {2,7,2,5}*280
   7-fold quotients : {2,4,2,5}*160
   14-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)
(25,28)(26,27)(29,30);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)
(20,29)(22,26)(24,27)(28,30);;
s3 := (32,33)(34,35);;
s4 := (31,32)(33,34);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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*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(35)!(1,2);
s1 := Sym(35)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)
(23,24)(25,28)(26,27)(29,30);
s2 := Sym(35)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)
(18,21)(20,29)(22,26)(24,27)(28,30);
s3 := Sym(35)!(32,33)(34,35);
s4 := Sym(35)!(31,32)(33,34);
poly := sub<Sym(35)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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*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