Polytope of Type {6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,30}*720a
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 3
Schlafli Type : {6,30}
Number of vertices, edges, etc : 12, 180, 60
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,30,2} of size 1440
Vertex Figure Of :
   {2,6,30} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,15}*360
   3-fold quotients : {6,10}*240c
   6-fold quotients : {3,10}*120b, {6,5}*120c
   12-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,60}*1440a, {6,60}*1440b, {6,30}*1440f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope