Polytope of Type {45,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {45,6}*1080
if this polytope has a name.
Group : SmallGroup(1080,263)
Rank : 3
Schlafli Type : {45,6}
Number of vertices, edges, etc : 90, 270, 12
Order of s₀s₁s₂ : 45
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {15,6}*360
   9-fold quotients : {5,6}*120b
   18-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 4)( 3, 6)( 5, 8)( 7, 9)(11,12)(13,14);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)(10,11)(12,13);;
s2 := (11,14)(12,13);;
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*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!( 2, 4)( 3, 6)( 5, 8)( 7, 9)(11,12)(13,14);
s1 := Sym(14)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)(10,11)(12,13);
s2 := Sym(14)!(11,14)(12,13);
poly := sub<Sym(14)|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*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 >;

References : None.
to this polytope