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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,2,2,7}*784
if this polytope has a name.
Group : SmallGroup(784,169)
Rank : 6
Schlafli Type : {7,2,2,2,7}
Number of vertices, edges, etc : 7, 7, 2, 2, 7, 7
Order of s₀s₁s₂s₃s₄s₅ : 14
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,2,2,7,2} of size 1568
Vertex Figure Of :
   {2,7,2,2,2,7} of size 1568
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,4,2,7}*1568, {7,2,2,2,14}*1568, {14,2,2,2,7}*1568
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (8,9);;
s3 := (10,11);;
s4 := (13,14)(15,16)(17,18);;
s5 := (12,13)(14,15)(16,17);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!(2,3)(4,5)(6,7);
s1 := Sym(18)!(1,2)(3,4)(5,6);
s2 := Sym(18)!(8,9);
s3 := Sym(18)!(10,11);
s4 := Sym(18)!(13,14)(15,16)(17,18);
s5 := Sym(18)!(12,13)(14,15)(16,17);
poly := sub<Sym(18)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope