Polytope of Type {2,14,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,4}*784
if this polytope has a name.
Group : SmallGroup(784,165)
Rank : 4
Schlafli Type : {2,14,4}
Number of vertices, edges, etc : 2, 49, 98, 14
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,4,2} of size 1568
Vertex Figure Of :
   {2,2,14,4} of size 1568
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,14,4}*1568
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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