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Polytope of Type {16,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,2,9}*576
if this polytope has a name.
Group : SmallGroup(576,472)
Rank : 4
Schlafli Type : {16,2,9}
Number of vertices, edges, etc : 16, 16, 9, 9
Order of s0s1s2s3 : 144
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {16,2,9,2} of size 1152
Vertex Figure Of :
   {2,16,2,9} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,2,9}*288
   3-fold quotients : {16,2,3}*192
   4-fold quotients : {4,2,9}*144
   6-fold quotients : {8,2,3}*96
   8-fold quotients : {2,2,9}*72
   12-fold quotients : {4,2,3}*48
   24-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {32,2,9}*1152, {16,2,18}*1152
   3-fold covers : {16,2,27}*1728, {48,2,9}*1728, {16,6,9}*1728
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := (18,19)(20,21)(22,23)(24,25);;
s3 := (17,18)(19,20)(21,22)(23,24);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(25)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(25)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(25)!(18,19)(20,21)(22,23)(24,25);
s3 := Sym(25)!(17,18)(19,20)(21,22)(23,24);
poly := sub<Sym(25)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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