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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,14,4}*1568
if this polytope has a name.
Group : SmallGroup(1568,921)
Rank : 5
Schlafli Type : {2,2,14,4}
Number of vertices, edges, etc : 2, 2, 49, 98, 14
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(12,47)(13,53)(14,52)(15,51)(16,50)(17,49)(18,48)
(19,40)(20,46)(21,45)(22,44)(23,43)(24,42)(25,41)(26,33)(27,39)(28,38)(29,37)
(30,36)(31,35)(32,34);;
s3 := ( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(10,17)(11,18)(19,47)(20,48)(21,49)
(22,50)(23,51)(24,52)(25,53)(26,40)(27,41)(28,42)(29,43)(30,44)(31,45)
(32,46);;
s4 := ( 6,12)( 7,19)( 8,26)( 9,33)(10,40)(11,47)(14,20)(15,27)(16,34)(17,41)
(18,48)(22,28)(23,35)(24,42)(25,49)(30,36)(31,43)(32,50)(38,44)(39,51)
(46,52);;
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, s1*s2*s1*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*s4*s3*s4, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*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)!(3,4);
s2 := Sym(53)!( 6,11)( 7,10)( 8, 9)(12,47)(13,53)(14,52)(15,51)(16,50)(17,49)
(18,48)(19,40)(20,46)(21,45)(22,44)(23,43)(24,42)(25,41)(26,33)(27,39)(28,38)
(29,37)(30,36)(31,35)(32,34);
s3 := Sym(53)!( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(10,17)(11,18)(19,47)(20,48)
(21,49)(22,50)(23,51)(24,52)(25,53)(26,40)(27,41)(28,42)(29,43)(30,44)(31,45)
(32,46);
s4 := Sym(53)!( 6,12)( 7,19)( 8,26)( 9,33)(10,40)(11,47)(14,20)(15,27)(16,34)
(17,41)(18,48)(22,28)(23,35)(24,42)(25,49)(30,36)(31,43)(32,50)(38,44)(39,51)
(46,52);
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, 
s1*s2*s1*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*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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