Polytope of Type {35,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,10}*840
if this polytope has a name.
Group : SmallGroup(840,137)
Rank : 3
Schlafli Type : {35,10}
Number of vertices, edges, etc : 42, 210, 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 :
   {35,10,2} of size 1680
Vertex Figure Of :
   {2,35,10} of size 1680
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {5,10}*120a
   14-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {35,10}*1680, {70,10}*1680a, {70,10}*1680b
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);;
s2 := ( 9,11)(10,12);;
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, 
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!( 2, 3)( 4, 5)( 6, 7)( 9,10)(11,12);
s1 := Sym(12)!( 1, 2)( 3, 4)( 5, 6)( 8, 9)(10,11);
s2 := Sym(12)!( 9,11)(10,12);
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, 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, 
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 >; 
 
References : None.
to this polytope