Polytope of Type {10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*720
if this polytope has a name.
Group : SmallGroup(720,767)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 30, 180, 36
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,12,2} of size 1440
Vertex Figure Of :
   {2,10,12} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,4}*240a
   6-fold quotients : {5,4}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,12}*1440b, {10,12}*1440d, {10,12}*1440g
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope