Polytope of Type {30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,5849)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 180, 360, 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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,4}*720
   3-fold quotients : {10,4}*480c
   6-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
   12-fold quotients : {5,4}*120
   60-fold quotients : {6,2}*24
   120-fold quotients : {3,2}*12
   180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 2)( 3, 5)( 4, 6)( 8, 9)(10,11);;
s1 := ( 2, 6)( 4, 5)( 7, 8)( 9,10);;
s2 := (8,9);;
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, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope