Polytope of Type {35,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,6}*1680a
if this polytope has a name.
Group : SmallGroup(1680,924)
Rank : 3
Schlafli Type : {35,6}
Number of vertices, edges, etc : 140, 420, 24
Order of s₀s₁s₂ : 35
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {7,6}*336
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 7)( 3, 8)( 5, 6)(10,11)(12,13);;
s1 := ( 3, 6)( 4, 5)( 7, 8)( 9,10)(11,12);;
s2 := (1,4)(2,7)(3,6)(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*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!( 2, 7)( 3, 8)( 5, 6)(10,11)(12,13);
s1 := Sym(13)!( 3, 6)( 4, 5)( 7, 8)( 9,10)(11,12);
s2 := Sym(13)!(1,4)(2,7)(3,6)(5,8);
poly := sub<Sym(13)|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*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope