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Polytope of Type {10,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,21}*1680
if this polytope has a name.
Group : SmallGroup(1680,931)
Rank : 3
Schlafli Type : {10,21}
Number of vertices, edges, etc : 40, 420, 84
Order of s0s1s2 : 70
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,21}*840
   7-fold quotients : {10,3}*240
   14-fold quotients : {5,3}*120, {10,3}*120a, {10,3}*120b
   28-fold quotients : {5,3}*60
   60-fold quotients : {2,7}*28
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9,10)(11,12)(13,14);;
s1 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 9,12)(10,11);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!( 9,10)(11,12)(13,14);
s1 := Sym(14)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(14)!( 1, 2)( 3, 4)( 5, 6)( 9,12)(10,11);
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope