Polytope of Type {3,7}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope