Polytope of Type {4,8,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,2,9}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97511)
Rank : 5
Schlafli Type : {4,8,2,9}
Number of vertices, edges, etc : 4, 16, 8, 9, 9
Order of s0s1s2s3s4 : 72
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 : {4,4,2,9}*576, {2,8,2,9}*576
   3-fold quotients : {4,8,2,3}*384a
   4-fold quotients : {2,4,2,9}*288, {4,2,2,9}*288
   6-fold quotients : {4,4,2,3}*192, {2,8,2,3}*192
   8-fold quotients : {2,2,2,9}*144
   12-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96
   24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := ( 2, 4)( 3, 6)(10,13)(12,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);;
s2 := ( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);;
s3 := (18,19)(20,21)(22,23)(24,25);;
s4 := (17,18)(19,20)(21,22)(23,24);;
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(25)!( 2, 4)( 3, 6)(10,13)(12,15);
s1 := Sym(25)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);
s2 := Sym(25)!( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);
s3 := Sym(25)!(18,19)(20,21)(22,23)(24,25);
s4 := Sym(25)!(17,18)(19,20)(21,22)(23,24);
poly := sub<Sym(25)|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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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 >;

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