Polytope of Type {2,3,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12}*1296
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 4
Schlafli Type : {2,3,12}
Number of vertices, edges, etc : 2, 27, 162, 108
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 := ( 4,21)( 5,12)( 6, 9)( 7,27)( 8,18)(10,24)(11,15)(13,23)(16,29)(17,20)
(19,26)(25,28);;
s3 := ( 3,24)( 4,25)( 5,26)( 6,21)( 7,22)( 8,23)( 9,27)(10,28)(11,29)(12,15)
(13,16)(14,17);;
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*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*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)!( 4,21)( 5,12)( 6, 9)( 7,27)( 8,18)(10,24)(11,15)(13,23)(16,29)
(17,20)(19,26)(25,28);
s3 := Sym(29)!( 3,24)( 4,25)( 5,26)( 6,21)( 7,22)( 8,23)( 9,27)(10,28)(11,29)
(12,15)(13,16)(14,17);
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*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3 >;

to this polytope