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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,9,2,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,46164)
Rank : 7
Schlafli Type : {2,2,6,9,2,2}
Number of vertices, edges, etc : 2, 2, 6, 27, 9, 2, 2
Order of s₀s₁s₂s₃s₄s₅s₆ : 18
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 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 : {2,2,2,9,2,2}*576, {2,2,6,3,2,2}*576
   9-fold quotients : {2,2,2,3,2,2}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

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