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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,7,2}*784
if this polytope has a name.
Group : SmallGroup(784,169)
Rank : 5
Schlafli Type : {2,14,7,2}
Number of vertices, edges, etc : 2, 14, 49, 7, 2
Order of s0s1s2s3s4 : 14
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,7,2,2} of size 1568
Vertex Figure Of :
   {2,2,14,7,2} of size 1568
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,2,7,2}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,14,7,2}*1568, {2,14,14,2}*1568b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (10,45)(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,38)(18,39)(19,40)
(20,41)(21,42)(22,43)(23,44)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)
(30,37);;
s2 := ( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(17,45)(18,51)(19,50)
(20,49)(21,48)(22,47)(23,46)(24,38)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)
(32,37)(33,36)(34,35);;
s3 := ( 3, 4)( 5, 9)( 6, 8)(10,46)(11,45)(12,51)(13,50)(14,49)(15,48)(16,47)
(17,39)(18,38)(19,44)(20,43)(21,42)(22,41)(23,40)(24,32)(25,31)(26,37)(27,36)
(28,35)(29,34)(30,33);;
s4 := (52,53);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(53)!(1,2);
s1 := Sym(53)!(10,45)(11,46)(12,47)(13,48)(14,49)(15,50)(16,51)(17,38)(18,39)
(19,40)(20,41)(21,42)(22,43)(23,44)(24,31)(25,32)(26,33)(27,34)(28,35)(29,36)
(30,37);
s2 := Sym(53)!( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(17,45)(18,51)
(19,50)(20,49)(21,48)(22,47)(23,46)(24,38)(25,44)(26,43)(27,42)(28,41)(29,40)
(30,39)(32,37)(33,36)(34,35);
s3 := Sym(53)!( 3, 4)( 5, 9)( 6, 8)(10,46)(11,45)(12,51)(13,50)(14,49)(15,48)
(16,47)(17,39)(18,38)(19,44)(20,43)(21,42)(22,41)(23,40)(24,32)(25,31)(26,37)
(27,36)(28,35)(29,34)(30,33);
s4 := Sym(53)!(52,53);
poly := sub<Sym(53)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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