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Polytope of Type {6,2,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2,4,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,46115)
Rank : 6
Schlafli Type : {6,2,2,4,9}
Number of vertices, edges, etc : 6, 6, 2, 4, 18, 9
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {3,2,2,4,9}*864
   3-fold quotients : {2,2,2,4,9}*576, {6,2,2,4,3}*576
   6-fold quotients : {3,2,2,4,3}*288
   9-fold quotients : {2,2,2,4,3}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
s3 := (10,15)(11,17)(12,19)(13,21)(16,26)(18,28)(22,32)(29,38)(31,40)(33,41)
(35,42)(37,43);;
s4 := ( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)(26,32)
(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);;
s5 := ( 9,14)(10,12)(11,22)(13,18)(15,19)(16,31)(17,32)(20,27)(21,28)(23,24)
(25,39)(26,40)(29,35)(30,36)(33,37)(34,44)(38,42)(41,43);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(44)!(3,4)(5,6);
s1 := Sym(44)!(1,5)(2,3)(4,6);
s2 := Sym(44)!(7,8);
s3 := Sym(44)!(10,15)(11,17)(12,19)(13,21)(16,26)(18,28)(22,32)(29,38)(31,40)
(33,41)(35,42)(37,43);
s4 := Sym(44)!( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)
(26,32)(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);
s5 := Sym(44)!( 9,14)(10,12)(11,22)(13,18)(15,19)(16,31)(17,32)(20,27)(21,28)
(23,24)(25,39)(26,40)(29,35)(30,36)(33,37)(34,44)(38,42)(41,43);
poly := sub<Sym(44)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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