Polytope of Type {4,2,15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,15,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,240151)
Rank : 5
Schlafli Type : {4,2,15,6}
Number of vertices, edges, etc : 4, 4, 20, 60, 8
Order of s₀s₁s₂s₃s₄ : 20
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 : {2,2,15,6}*960
   5-fold quotients : {4,2,3,6}*384
   10-fold quotients : {4,2,3,3}*192, {2,2,3,6}*192
   12-fold quotients : {4,2,5,2}*160
   20-fold quotients : {2,2,3,3}*96
   24-fold quotients : {2,2,5,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,21)(10,22)(11,24)(12,23)(13,17)(14,18)(15,20)(16,19);;
s3 := ( 5, 9)( 6,11)( 7,10)( 8,12)(13,21)(14,23)(15,22)(16,24)(18,19);;
s4 := ( 5, 6)( 9,10)(13,14)(17,18)(21,22);;
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*s0*s1, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s3*s2*s3*s2*s4*s3*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(24)!(2,3);
s1 := Sym(24)!(1,2)(3,4);
s2 := Sym(24)!( 7, 8)( 9,21)(10,22)(11,24)(12,23)(13,17)(14,18)(15,20)(16,19);
s3 := Sym(24)!( 5, 9)( 6,11)( 7,10)( 8,12)(13,21)(14,23)(15,22)(16,24)(18,19);
s4 := Sym(24)!( 5, 6)( 9,10)(13,14)(17,18)(21,22);
poly := sub<Sym(24)|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*s0*s1, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s3*s2*s3*s2*s4*s3*s2*s3*s4*s2*s3 >;

to this polytope