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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,9,2}*864
if this polytope has a name.
Group : SmallGroup(864,4032)
Rank : 6
Schlafli Type : {2,2,6,9,2}
Number of vertices, edges, etc : 2, 2, 6, 27, 9, 2
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,6,9,2,2} of size 1728
Vertex Figure Of :
   {2,2,2,6,9,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,9,2}*288, {2,2,6,3,2}*288
   9-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,6,9,2}*1728, {2,4,6,9,2}*1728, {2,2,6,18,2}*1728b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(28,29)(30,31);;
s3 := ( 5, 8)( 6,14)( 7,11)(10,20)(12,15)(13,17)(16,26)(18,21)(19,23)(22,30)
(24,27)(25,28)(29,31);;
s4 := ( 5, 6)( 7,10)( 8,12)( 9,11)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)
(26,29)(27,28)(30,31);;
s5 := (32,33);;
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*s1*s0*s1, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
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)!(1,2);
s1 := Sym(33)!(3,4);
s2 := Sym(33)!( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(28,29)(30,31);
s3 := Sym(33)!( 5, 8)( 6,14)( 7,11)(10,20)(12,15)(13,17)(16,26)(18,21)(19,23)
(22,30)(24,27)(25,28)(29,31);
s4 := Sym(33)!( 5, 6)( 7,10)( 8,12)( 9,11)(13,16)(14,18)(15,17)(19,22)(20,24)
(21,23)(26,29)(27,28)(30,31);
s5 := Sym(33)!(32,33);
poly := sub<Sym(33)|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*s1*s0*s1, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
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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