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Polytope of Type {7,2,4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,4,14}*1568
if this polytope has a name.
Group : SmallGroup(1568,858)
Rank : 5
Schlafli Type : {7,2,4,14}
Number of vertices, edges, etc : 7, 7, 4, 28, 14
Order of s0s1s2s3s4 : 28
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 : {7,2,2,14}*784
   4-fold quotients : {7,2,2,7}*392
   7-fold quotients : {7,2,4,2}*224
   14-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,12)(13,18)(14,19)(20,26)(21,27)(28,32)(29,33);;
s3 := ( 8, 9)(10,14)(11,13)(12,17)(15,21)(16,20)(18,25)(19,24)(22,29)(23,28)
(26,31)(27,30)(32,35)(33,34);;
s4 := ( 8,10)( 9,13)(11,15)(12,18)(14,20)(16,22)(17,24)(19,26)(21,28)(25,30)
(27,32)(31,34);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(35)!(2,3)(4,5)(6,7);
s1 := Sym(35)!(1,2)(3,4)(5,6);
s2 := Sym(35)!( 9,12)(13,18)(14,19)(20,26)(21,27)(28,32)(29,33);
s3 := Sym(35)!( 8, 9)(10,14)(11,13)(12,17)(15,21)(16,20)(18,25)(19,24)(22,29)
(23,28)(26,31)(27,30)(32,35)(33,34);
s4 := Sym(35)!( 8,10)( 9,13)(11,15)(12,18)(14,20)(16,22)(17,24)(19,26)(21,28)
(25,30)(27,32)(31,34);
poly := sub<Sym(35)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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