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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,9,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,46114)
Rank : 5
Schlafli Type : {2,6,9,2}
Number of vertices, edges, etc : 2, 24, 108, 36, 2
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,6,3,2}*576
   4-fold quotients : {2,6,9,2}*432
   9-fold quotients : {2,6,3,2}*192
   12-fold quotients : {2,2,9,2}*144, {2,6,3,2}*144
   18-fold quotients : {2,3,3,2}*96
   36-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope