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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,2,6}*672
if this polytope has a name.
Group : SmallGroup(672,1271)
Rank : 5
Schlafli Type : {2,14,2,6}
Number of vertices, edges, etc : 2, 14, 14, 6, 6
Order of s0s1s2s3s4 : 42
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,2,6,2} of size 1344
Vertex Figure Of :
   {2,2,14,2,6} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,7,2,6}*336, {2,14,2,3}*336
   3-fold quotients : {2,14,2,2}*224
   4-fold quotients : {2,7,2,3}*168
   6-fold quotients : {2,7,2,2}*112
   7-fold quotients : {2,2,2,6}*96
   14-fold quotients : {2,2,2,3}*48
   21-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,14,2,12}*1344, {2,28,2,6}*1344, {2,14,4,6}*1344, {4,14,2,6}*1344
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 := (19,20)(21,22);;
s4 := (17,21)(18,19)(20,22);;
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*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*s3*s4*s3*s4*s3*s4*s3*s4, 
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(22)!(1,2);
s1 := Sym(22)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(22)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,16);
s3 := Sym(22)!(19,20)(21,22);
s4 := Sym(22)!(17,21)(18,19)(20,22);
poly := sub<Sym(22)|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*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*s3*s4*s3*s4*s3*s4*s3*s4, 
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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