Polytope of Type {3,2,6,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,15}*1440
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 5
Schlafli Type : {3,2,6,15}
Number of vertices, edges, etc : 3, 3, 8, 60, 20
Order of s₀s₁s₂s₃s₄ : 60
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) :
   5-fold quotients : {3,2,6,3}*288
   10-fold quotients : {3,2,3,3}*144
   12-fold quotients : {3,2,2,5}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope