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Polytope of Type {6,3,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3,4,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1088539)
Rank : 5
Schlafli Type : {6,3,4,2}
Number of vertices, edges, etc : 8, 24, 16, 8, 2
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {3,3,4,2}*384
   8-fold quotients : {3,3,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (3,5)(4,6);;
s1 := (1,2)(3,4)(5,8)(6,7);;
s2 := (1,7)(2,8)(3,4)(5,6);;
s3 := (3,4)(5,6)(7,8);;
s4 := ( 9,10);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s3*s1*s2*s3*s1*s2*s0*s3*s1*s2*s3*s2*s0*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(3,5)(4,6);
s1 := Sym(10)!(1,2)(3,4)(5,8)(6,7);
s2 := Sym(10)!(1,7)(2,8)(3,4)(5,6);
s3 := Sym(10)!(3,4)(5,6)(7,8);
s4 := Sym(10)!( 9,10);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s3*s1*s2*s3*s1*s2*s0*s3*s1*s2*s3*s2*s0*s1*s2 >; 
 

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