Questions?
See the FAQ
or other info.

Polytope of Type {7,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,9}*1008a
if this polytope has a name.
Group : SmallGroup(1008,880)
Rank : 3
Schlafli Type : {7,9}
Number of vertices, edges, etc : 56, 252, 72
Order of s0s1s2 : 14
Order of s0s1s2s1 : 7
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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) :
   2-fold quotients : {7,9}*504c
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 7)( 5, 6)( 8, 9)(10,11);;
s1 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)(10,11);;
s2 := ( 2, 4)( 3, 7)( 5, 9)( 6, 8)(10,11);;
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(11)!( 2, 3)( 4, 7)( 5, 6)( 8, 9)(10,11);
s1 := Sym(11)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)(10,11);
s2 := Sym(11)!( 2, 4)( 3, 7)( 5, 9)( 6, 8)(10,11);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0 >; 
 
References : None.
to this polytope