Polytope of Type {10,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,21}*840
if this polytope has a name.
Group : SmallGroup(840,137)
Rank : 3
Schlafli Type : {10,21}
Number of vertices, edges, etc : 20, 210, 42
Order of s₀s₁s₂ : 35
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,21,2} of size 1680
Vertex Figure Of :
   {2,10,21} of size 1680
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {10,3}*120b
   14-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,21}*1680, {10,42}*1680b, {10,42}*1680c
Permutation Representation (GAP) :

s0 := ( 9,10)(11,12);;
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*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope