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

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

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

Permutation Representation (Magma) :

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

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