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Polytope of Type {9,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,7}*504c
Also Known As : {9,7}3if this polytope has another name.
Group : SmallGroup(504,156)
Rank : 3
Schlafli Type : {9,7}
Number of vertices, edges, etc : 36, 126, 28
Order of s0s1s2 : 3
Order of s0s1s2s1 : 9
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {9,7,2} of size 1008
Vertex Figure Of :
   {2,9,7} of size 1008
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,7}*1008b, {9,14}*1008b, {9,14}*1008e, {18,7}*1008b, {18,7}*1008e
Permutation Representation (GAP) :
s0 := (2,3)(4,6)(5,8)(7,9);;
s1 := (1,2)(3,4)(6,7)(8,9);;
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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(9)!(2,3)(4,6)(5,8)(7,9);
s1 := Sym(9)!(1,2)(3,4)(6,7)(8,9);
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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope