Polytope of Type {2,10,35}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,35}*1680
if this polytope has a name.
Group : SmallGroup(1680,931)
Rank : 4
Schlafli Type : {2,10,35}
Number of vertices, edges, etc : 2, 12, 210, 42
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,10,5}*240b
   14-fold quotients : {2,5,5}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (11,12)(13,14);;
s2 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s3 := ( 3, 4)( 5, 6)( 7, 8)(11,13)(12,14);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!(1,2);
s1 := Sym(14)!(11,12)(13,14);
s2 := Sym(14)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s3 := Sym(14)!( 3, 4)( 5, 6)( 7, 8)(11,13)(12,14);
poly := sub<Sym(14)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1 >;

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