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Polytope of Type {2,9,2,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,2,16}*1152
if this polytope has a name.
Group : SmallGroup(1152,133439)
Rank : 5
Schlafli Type : {2,9,2,16}
Number of vertices, edges, etc : 2, 9, 9, 16, 16
Order of s0s1s2s3s4 : 144
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 : {2,9,2,8}*576
   3-fold quotients : {2,3,2,16}*384
   4-fold quotients : {2,9,2,4}*288
   6-fold quotients : {2,3,2,8}*192
   8-fold quotients : {2,9,2,2}*144
   12-fold quotients : {2,3,2,4}*96
   24-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
s4 := (12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(27)!(1,2);
s1 := Sym(27)!( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(27)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(27)!(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
s4 := Sym(27)!(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);
poly := sub<Sym(27)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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