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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,9,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,46114)
Rank : 5
Schlafli Type : {2,2,9,6}
Number of vertices, edges, etc : 2, 2, 36, 108, 24
Order of s0s1s2s3s4 : 36
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) :
   3-fold quotients : {2,2,3,6}*576
   4-fold quotients : {2,2,9,6}*432
   9-fold quotients : {2,2,3,6}*192
   12-fold quotients : {2,2,9,2}*144, {2,2,3,6}*144
   18-fold quotients : {2,2,3,3}*96
   36-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,13)(10,15)(11,14)(12,16)(17,33)(18,35)(19,34)(20,36)(21,29)
(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40);;
s3 := ( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)(14,22)
(15,24)(16,23)(29,33)(30,34)(31,36)(32,35)(39,40);;
s4 := ( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28)(29,32)(33,36)(37,40);;
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*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, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3*s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 6, 7)( 9,13)(10,15)(11,14)(12,16)(17,33)(18,35)(19,34)(20,36)
(21,29)(22,31)(23,30)(24,32)(25,37)(26,39)(27,38)(28,40);
s3 := Sym(40)!( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)(11,28)(12,27)(13,21)
(14,22)(15,24)(16,23)(29,33)(30,34)(31,36)(32,35)(39,40);
s4 := Sym(40)!( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28)(29,32)(33,36)(37,40);
poly := sub<Sym(40)|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*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, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3*s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 >; 
 

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