Polytope of Type {2,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,4}*512b
if this polytope has a name.
Group : SmallGroup(512,420049)
Rank : 4
Schlafli Type : {2,8,4}
Number of vertices, edges, etc : 2, 32, 64, 16
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,8,4}*256b
   4-fold quotients : {2,4,4}*128
   8-fold quotients : {2,4,4}*64
   16-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,15)( 4,16)( 5,18)( 6,17)( 7,11)( 8,12)( 9,14)(10,13);;
s2 := ( 7, 9)( 8,10)(13,14)(15,16)(17,18);;
s3 := ( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 3,15)( 4,16)( 5,18)( 6,17)( 7,11)( 8,12)( 9,14)(10,13);
s2 := Sym(18)!( 7, 9)( 8,10)(13,14)(15,16)(17,18);
s3 := Sym(18)!( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)( 9,17)(10,18);
poly := sub<Sym(18)|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 >;

to this polytope