Polytope of Type {2,4,8,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,8,2,7}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1035859)
Rank : 6
Schlafli Type : {2,4,8,2,7}
Number of vertices, edges, etc : 2, 4, 16, 8, 7, 7
Order of s₀s₁s₂s₃s₄s₅ : 56
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {2,4,4,2,7}*896, {2,2,8,2,7}*896
   4-fold quotients : {2,2,4,2,7}*448, {2,4,2,2,7}*448
   8-fold quotients : {2,2,2,2,7}*224
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 6)( 5, 8)(12,15)(14,17);;
s2 := ( 3, 4)( 5, 7)( 6, 9)( 8,11)(10,12)(13,15)(14,16)(17,18);;
s3 := ( 4, 5)( 6, 8)( 7,10)(11,13)(12,14)(15,17);;
s4 := (20,21)(22,23)(24,25);;
s5 := (19,20)(21,22)(23,24);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(25)!(1,2);
s1 := Sym(25)!( 4, 6)( 5, 8)(12,15)(14,17);
s2 := Sym(25)!( 3, 4)( 5, 7)( 6, 9)( 8,11)(10,12)(13,15)(14,16)(17,18);
s3 := Sym(25)!( 4, 5)( 6, 8)( 7,10)(11,13)(12,14)(15,17);
s4 := Sym(25)!(20,21)(22,23)(24,25);
s5 := Sym(25)!(19,20)(21,22)(23,24);
poly := sub<Sym(25)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope