Polytope of Type {4,2,2,6,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,6,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,30790)
Rank : 6
Schlafli Type : {4,2,2,6,9}
Number of vertices, edges, etc : 4, 4, 2, 6, 27, 9
Order of s₀s₁s₂s₃s₄s₅ : 36
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   2-fold quotients : {2,2,2,6,9}*864
   3-fold quotients : {4,2,2,2,9}*576, {4,2,2,6,3}*576
   6-fold quotients : {2,2,2,2,9}*288, {2,2,2,6,3}*288
   9-fold quotients : {4,2,2,2,3}*192
   18-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope