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Polytope of Type {11,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,4,9}*1584
if this polytope has a name.
Group : SmallGroup(1584,364)
Rank : 5
Schlafli Type : {11,2,4,9}
Number of vertices, edges, etc : 11, 11, 4, 18, 9
Order of s0s1s2s3s4 : 99
Order of s0s1s2s3s4s3s2s1 : 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) :
   3-fold quotients : {11,2,4,3}*528
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := (13,18)(14,20)(15,22)(16,24)(19,29)(21,31)(25,35)(32,41)(34,43)(36,44)
(38,45)(40,46);;
s3 := (12,13)(14,17)(15,16)(18,26)(19,25)(20,27)(21,23)(22,24)(28,34)(29,35)
(30,32)(31,33)(36,42)(37,43)(38,40)(39,41)(44,47)(45,46);;
s4 := (12,17)(13,15)(14,25)(16,21)(18,22)(19,34)(20,35)(23,30)(24,31)(26,27)
(28,42)(29,43)(32,38)(33,39)(36,40)(37,47)(41,45)(44,46);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(47)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(47)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(47)!(13,18)(14,20)(15,22)(16,24)(19,29)(21,31)(25,35)(32,41)(34,43)
(36,44)(38,45)(40,46);
s3 := Sym(47)!(12,13)(14,17)(15,16)(18,26)(19,25)(20,27)(21,23)(22,24)(28,34)
(29,35)(30,32)(31,33)(36,42)(37,43)(38,40)(39,41)(44,47)(45,46);
s4 := Sym(47)!(12,17)(13,15)(14,25)(16,21)(18,22)(19,34)(20,35)(23,30)(24,31)
(26,27)(28,42)(29,43)(32,38)(33,39)(36,40)(37,47)(41,45)(44,46);
poly := sub<Sym(47)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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