Polytope of Type {7,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,3}*336
Also Known As : {7,3}₈. if this polytope has another name.
Group : SmallGroup(336,208)
Rank : 3
Schlafli Type : {7,3}
Number of vertices, edges, etc : 56, 84, 24
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 7
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {7,3,2} of size 672
Vertex Figure Of :
   {2,7,3} of size 672
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,6}*672a, {14,3}*672
   3-fold covers : {21,3}*1008
   4-fold covers : {7,12}*1344, {28,3}*1344, {14,6}*1344b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope