Polytope of Type {5,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,5,2}*1440
if this polytope has a name.
Group : SmallGroup(1440,5843)
Rank : 4
Schlafli Type : {5,5,2}
Number of vertices, edges, etc : 72, 180, 72, 2
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 8)( 4,10)( 5, 6)( 7, 9);;
s1 := ( 1, 2)( 3, 4)( 5, 9)( 6, 8)( 7,10);;
s2 := ( 1, 3)( 2, 7)( 4, 5)( 6,10)( 8, 9);;
s3 := (11,12);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(12)!( 1, 3)( 2, 8)( 4,10)( 5, 6)( 7, 9);
s1 := Sym(12)!( 1, 2)( 3, 4)( 5, 9)( 6, 8)( 7,10);
s2 := Sym(12)!( 1, 3)( 2, 7)( 4, 5)( 6,10)( 8, 9);
s3 := Sym(12)!(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

to this polytope