Polytope of Type {70,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,10}*1680b
if this polytope has a name.
Group : SmallGroup(1680,931)
Rank : 3
Schlafli Type : {70,10}
Number of vertices, edges, etc : 84, 420, 12
Order of s₀s₁s₂ : 21
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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) :
   2-fold quotients : {35,10}*840
   7-fold quotients : {10,10}*240d
   14-fold quotients : {5,10}*120a, {10,5}*120b
   28-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 9,10)(11,12);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 8, 9)(10,11)(13,14);;
s2 := ( 9,11)(10,12)(13,14);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!( 2, 3)( 4, 5)( 6, 7)( 9,10)(11,12);
s1 := Sym(14)!( 1, 2)( 3, 4)( 5, 6)( 8, 9)(10,11)(13,14);
s2 := Sym(14)!( 9,11)(10,12)(13,14);
poly := sub<Sym(14)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope