Polytope of Type {2,12,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4,2}*864
if this polytope has a name.
Group : SmallGroup(864,4007)
Rank : 5
Schlafli Type : {2,12,4,2}
Number of vertices, edges, etc : 2, 27, 54, 9, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,4,2,2} of size 1728
Vertex Figure Of :
   {2,2,12,4,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,4,4,2}*288
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,4,2}*1728a
Permutation Representation (GAP) : 
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19);;
s2 := ( 3,13)( 4,12)( 5,14)( 6,16)( 7,15)( 8,17)( 9,19)(10,18)(11,20);;
s3 := ( 3, 6)( 4, 8)( 5, 7)(10,11)(13,14)(15,16)(18,20);;
s4 := (21,22);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19);
s2 := Sym(22)!( 3,13)( 4,12)( 5,14)( 6,16)( 7,15)( 8,17)( 9,19)(10,18)(11,20);
s3 := Sym(22)!( 3, 6)( 4, 8)( 5, 7)(10,11)(13,14)(15,16)(18,20);
s4 := Sym(22)!(21,22);
poly := sub<Sym(22)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2 >;

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