Polytope of Type {2,2,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,16}*512b
if this polytope has a name.
Group : SmallGroup(512,7530027)
Rank : 5
Schlafli Type : {2,2,4,16}
Number of vertices, edges, etc : 2, 2, 4, 32, 16
Order of s0s1s2s3s4 : 16
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,4,8}*256a
   4-fold quotients : {2,2,4,4}*128, {2,2,2,8}*128
   8-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   16-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 9,10)(11,12)(17,18)(19,20);;
s3 := ( 7, 8)( 9,11)(10,12)(13,17)(14,18)(15,20)(16,19);;
s4 := ( 5,13)( 6,14)( 7,16)( 8,15)( 9,19)(10,20)(11,17)(12,18);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(20)!(1,2);
s1 := Sym(20)!(3,4);
s2 := Sym(20)!( 9,10)(11,12)(17,18)(19,20);
s3 := Sym(20)!( 7, 8)( 9,11)(10,12)(13,17)(14,18)(15,20)(16,19);
s4 := Sym(20)!( 5,13)( 6,14)( 7,16)( 8,15)( 9,19)(10,20)(11,17)(12,18);
poly := sub<Sym(20)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3 >;

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