Polytope of Type {2,4,9,2,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,9,2,3,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,46115)
Rank : 7
Schlafli Type : {2,4,9,2,3,2}
Number of vertices, edges, etc : 2, 4, 18, 9, 3, 3, 2
Order of s₀s₁s₂s₃s₄s₅s₆ : 18
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 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 : {2,4,3,2,3,2}*576
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 9)( 5,11)( 6,13)( 7,15)(10,20)(12,22)(16,26)(23,32)(25,34)(27,35)
(29,36)(31,37);;
s2 := ( 3, 4)( 5, 8)( 6, 7)( 9,17)(10,16)(11,18)(12,14)(13,15)(19,25)(20,26)
(21,23)(22,24)(27,33)(28,34)(29,31)(30,32)(35,38)(36,37);;
s3 := ( 3, 8)( 4, 6)( 5,16)( 7,12)( 9,13)(10,25)(11,26)(14,21)(15,22)(17,18)
(19,33)(20,34)(23,29)(24,30)(27,31)(28,38)(32,36)(35,37);;
s4 := (40,41);;
s5 := (39,40);;
s6 := (42,43);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6, 
s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(43)!(1,2);
s1 := Sym(43)!( 4, 9)( 5,11)( 6,13)( 7,15)(10,20)(12,22)(16,26)(23,32)(25,34)
(27,35)(29,36)(31,37);
s2 := Sym(43)!( 3, 4)( 5, 8)( 6, 7)( 9,17)(10,16)(11,18)(12,14)(13,15)(19,25)
(20,26)(21,23)(22,24)(27,33)(28,34)(29,31)(30,32)(35,38)(36,37);
s3 := Sym(43)!( 3, 8)( 4, 6)( 5,16)( 7,12)( 9,13)(10,25)(11,26)(14,21)(15,22)
(17,18)(19,33)(20,34)(23,29)(24,30)(27,31)(28,38)(32,36)(35,37);
s4 := Sym(43)!(40,41);
s5 := Sym(43)!(39,40);
s6 := Sym(43)!(42,43);
poly := sub<Sym(43)|s0,s1,s2,s3,s4,s5,s6>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s5*s6*s5*s6, s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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