Polytope of Type {7,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,3}*504
Also Known As : {7,3}₉. if this polytope has another name.
Group : SmallGroup(504,156)
Rank : 3
Schlafli Type : {7,3}
Number of vertices, edges, etc : 84, 126, 36
Order of s₀s₁s₂ : 9
Order of s₀s₁s₂s₁ : 7
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {7,3,2} of size 1008
Vertex Figure Of :
   {2,7,3} of size 1008
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,3}*1008, {7,6}*1008a, {7,6}*1008b, {14,3}*1008a, {14,3}*1008b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope