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Polytope of Type {2,15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,5849)
Rank : 4
Schlafli Type : {2,15,4}
Number of vertices, edges, etc : 2, 90, 180, 24
Order of s₀s₁s₂s₃ : 6
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) :
   3-fold quotients : {2,5,4}*480
   6-fold quotients : {2,5,4}*240
   60-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)( 9,10);;
s2 := (3,4)(6,7)(8,9);;
s3 := (7,8);;
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, s3*s1*s3*s1, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope