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Polytope of Type {14,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2,7}*392
if this polytope has a name.
Group : SmallGroup(392,41)
Rank : 4
Schlafli Type : {14,2,7}
Number of vertices, edges, etc : 14, 14, 7, 7
Order of s0s1s2s3 : 14
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,2,7,2} of size 784
Vertex Figure Of :
   {2,14,2,7} of size 784
   {4,14,2,7} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,7}*196
   7-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,2,7}*784, {14,2,14}*784
   3-fold covers : {14,2,21}*1176, {42,2,7}*1176
   4-fold covers : {56,2,7}*1568, {14,2,28}*1568, {28,2,14}*1568, {14,4,14}*1568
   5-fold covers : {14,2,35}*1960, {70,2,7}*1960
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);;
s2 := (16,17)(18,19)(20,21);;
s3 := (15,16)(17,18)(19,20);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s1 := Sym(21)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);
s2 := Sym(21)!(16,17)(18,19)(20,21);
s3 := Sym(21)!(15,16)(17,18)(19,20);
poly := sub<Sym(21)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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