Polytope of Type {2,9,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,12}*1296a
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 4
Schlafli Type : {2,9,12}
Number of vertices, edges, etc : 2, 27, 162, 36
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   27-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope