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Polytope of Type {6,35}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,35}*840
if this polytope has a name.
Group : SmallGroup(840,137)
Rank : 3
Schlafli Type : {6,35}
Number of vertices, edges, etc : 12, 210, 70
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 :
{6,35,2} of size 1680
Vertex Figure Of :
{2,6,35} of size 1680
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {6,5}*120c
14-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,35}*1680c, {6,70}*1680a, {6,70}*1680b
Permutation Representation (GAP) :
s0 := ( 9,10)(11,12);;
s1 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(11,12);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(12)!( 9,10)(11,12);
s1 := Sym(12)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(11,12);
s2 := Sym(12)!( 1, 2)( 3, 4)( 5, 6)( 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope