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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,9,4}*1728
if this polytope has a name.
Group : SmallGroup(1728,46115)
Rank : 6
Schlafli Type : {2,6,2,9,4}
Number of vertices, edges, etc : 2, 6, 6, 9, 18, 4
Order of s₀s₁s₂s₃s₄s₅ : 18
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   2-fold quotients : {2,3,2,9,4}*864
   3-fold quotients : {2,2,2,9,4}*576, {2,6,2,3,4}*576
   6-fold quotients : {2,3,2,3,4}*288
   9-fold quotients : {2,2,2,3,4}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := ( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)(26,32)
(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);;
s4 := ( 9,13)(10,11)(12,20)(14,16)(15,17)(18,29)(19,30)(21,23)(22,25)(24,26)
(27,37)(28,38)(31,33)(32,34)(35,39)(36,43)(40,41)(42,44);;
s5 := ( 9,23)(10,15)(11,17)(14,24)(18,28)(20,30)(25,34)(27,36)(29,38)(31,40)
(33,41)(39,44);;
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*s1*s0*s1, s0*s2*s0*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, 
s4*s5*s4*s5*s4*s5*s4*s5, s5*s4*s3*s5*s4*s5*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(44)!(1,2);
s1 := Sym(44)!(5,6)(7,8);
s2 := Sym(44)!(3,7)(4,5)(6,8);
s3 := Sym(44)!( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)
(26,32)(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);
s4 := Sym(44)!( 9,13)(10,11)(12,20)(14,16)(15,17)(18,29)(19,30)(21,23)(22,25)
(24,26)(27,37)(28,38)(31,33)(32,34)(35,39)(36,43)(40,41)(42,44);
s5 := Sym(44)!( 9,23)(10,15)(11,17)(14,24)(18,28)(20,30)(25,34)(27,36)(29,38)
(31,40)(33,41)(39,44);
poly := sub<Sym(44)|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*s1*s0*s1, s0*s2*s0*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, s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s4*s3*s5*s4*s5*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope