Polytope of Type {15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4}*720
if this polytope has a name.
Group : SmallGroup(720,767)
Rank : 3
Schlafli Type : {15,4}
Number of vertices, edges, etc : 90, 180, 24
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {15,4,2} of size 1440
Vertex Figure Of :
   {2,15,4} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,4}*240
   6-fold quotients : {5,4}*120
   60-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,8}*1440, {30,4}*1440
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope