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Polytope of Type {2,14,2,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,2,2,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,11709)
Rank : 6
Schlafli Type : {2,14,2,2,6}
Number of vertices, edges, etc : 2, 14, 14, 2, 6, 6
Order of s0s1s2s3s4s5 : 42
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,7,2,2,6}*672, {2,14,2,2,3}*672
   3-fold quotients : {2,14,2,2,2}*448
   4-fold quotients : {2,7,2,2,3}*336
   6-fold quotients : {2,7,2,2,2}*224
   7-fold quotients : {2,2,2,2,6}*192
   14-fold quotients : {2,2,2,2,3}*96
   21-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,16);;
s3 := (17,18);;
s4 := (21,22)(23,24);;
s5 := (19,23)(20,21)(22,24);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(24)!(1,2);
s1 := Sym(24)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(24)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,16);
s3 := Sym(24)!(17,18);
s4 := Sym(24)!(21,22)(23,24);
s5 := Sym(24)!(19,23)(20,21)(22,24);
poly := sub<Sym(24)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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