Polytope of Type {4,4,2}

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

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

Permutation Representation (Magma) :

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

to this polytope