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

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

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