Polytope of Type {2,8,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,14}*1568a
if this polytope has a name.
Group : SmallGroup(1568,917)
Rank : 4
Schlafli Type : {2,8,14}
Number of vertices, edges, etc : 2, 28, 196, 49
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 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 := ( 4,34)( 5,16)( 6,40)( 7,22)( 8,46)( 9,28)(10,36)(12,42)(13,17)(14,48)
(15,30)(18,44)(20,50)(21,25)(23,31)(24,39)(26,45)(29,33)(32,47)(37,41)
(38,49);;
s2 := ( 4,11)( 5,19)( 6,27)( 7,35)( 8,43)( 9,51)(10,45)(13,20)(14,28)(15,36)
(16,44)(17,38)(18,46)(22,29)(23,37)(24,31)(25,39)(26,47)(33,40)(34,48)
(42,49);;
s3 := ( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,46)(18,45)(19,51)
(20,50)(21,49)(22,48)(23,47)(24,39)(25,38)(26,44)(27,43)(28,42)(29,41)(30,40)
(31,32)(33,37)(34,36);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope