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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,6,9}*1296
if this polytope has a name.
Group : SmallGroup(1296,2984)
Rank : 5
Schlafli Type : {6,2,6,9}
Number of vertices, edges, etc : 6, 6, 6, 27, 9
Order of s0s1s2s3s4 : 18
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 : {3,2,6,9}*648
   3-fold quotients : {2,2,6,9}*432, {6,2,2,9}*432, {6,2,6,3}*432
   6-fold quotients : {3,2,2,9}*216, {3,2,6,3}*216
   9-fold quotients : {2,2,2,9}*144, {2,2,6,3}*144, {6,2,2,3}*144
   18-fold quotients : {3,2,2,3}*72
   27-fold quotients : {2,2,2,3}*48
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 := (10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(30,31)(32,33);;
s3 := ( 7,10)( 8,16)( 9,13)(12,22)(14,17)(15,19)(18,28)(20,23)(21,25)(24,32)
(26,29)(27,30)(31,33);;
s4 := ( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(21,24)(22,26)(23,25)
(28,31)(29,30)(32,33);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(33)!(3,4)(5,6);
s1 := Sym(33)!(1,5)(2,3)(4,6);
s2 := Sym(33)!(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(30,31)(32,33);
s3 := Sym(33)!( 7,10)( 8,16)( 9,13)(12,22)(14,17)(15,19)(18,28)(20,23)(21,25)
(24,32)(26,29)(27,30)(31,33);
s4 := Sym(33)!( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(21,24)(22,26)
(23,25)(28,31)(29,30)(32,33);
poly := sub<Sym(33)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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