Polytope of Type {14,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,8,2}*1568a
if this polytope has a name.
Group : SmallGroup(1568,917)
Rank : 4
Schlafli Type : {14,8,2}
Number of vertices, edges, etc : 49, 196, 28, 2
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 := ( 2, 7)( 3, 6)( 4, 5)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)
(15,36)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,29)(23,35)(24,34)(25,33)
(26,32)(27,31)(28,30);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8,14)( 9,13)(10,12)(15,19)(16,18)(20,21)(22,24)
(25,28)(26,27)(30,35)(31,34)(32,33)(36,41)(37,40)(38,39)(43,46)(44,45)
(47,49);;
s2 := ( 2,12)( 3,16)( 4,27)( 5,31)( 6,42)( 7,46)( 8,28)( 9,32)(10,36)(11,47)
(14,17)(15,48)(19,22)(20,33)(21,37)(24,34)(25,38)(26,49)(29,39)(30,43)
(41,44);;
s3 := (50,51);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope