Polytope of Type {3,9,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,9,2}*1296
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 4
Schlafli Type : {3,9,2}
Number of vertices, edges, etc : 36, 162, 108, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   27-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope