Polytope of Type {7,2,9,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,9,6}*1512
if this polytope has a name.
Group : SmallGroup(1512,485)
Rank : 5
Schlafli Type : {7,2,9,6}
Number of vertices, edges, etc : 7, 7, 9, 27, 6
Order of s₀s₁s₂s₃s₄ : 126
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {7,2,9,2}*504, {7,2,3,6}*504
   9-fold quotients : {7,2,3,2}*168
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)(25,28)(26,30)
(27,29)(31,34)(32,33);;
s3 := ( 8,14)( 9,11)(10,20)(12,15)(13,17)(16,26)(18,21)(19,23)(22,31)(24,27)
(25,29)(28,33)(30,32);;
s4 := (11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(31,32)(33,34);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(34)!(2,3)(4,5)(6,7);
s1 := Sym(34)!(1,2)(3,4)(5,6);
s2 := Sym(34)!( 9,10)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)(25,28)
(26,30)(27,29)(31,34)(32,33);
s3 := Sym(34)!( 8,14)( 9,11)(10,20)(12,15)(13,17)(16,26)(18,21)(19,23)(22,31)
(24,27)(25,29)(28,33)(30,32);
s4 := Sym(34)!(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(31,32)(33,34);
poly := sub<Sym(34)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope