# Polytope of Type {4,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,6}*1296b
if this polytope has a name.
Group : SmallGroup(1296,3490)
Rank : 4
Schlafli Type : {4,3,6}
Number of vertices, edges, etc : 12, 54, 81, 27
Order of s0s1s2s3 : 9
Order of s0s1s2s3s2s1 : 6
Special Properties :
Locally Toroidal
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);;
s1 := ( 7,10)( 8,11)( 9,12);;
s2 := ( 4,10)( 5,12)( 6,11);;
s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s3*s0*s1*s2*s3*s2*s3*s2*s0*s1*s0 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);
s1 := Sym(12)!( 7,10)( 8,11)( 9,12);
s2 := Sym(12)!( 4,10)( 5,12)( 6,11);
s3 := Sym(12)!( 1, 2)( 4, 5)( 7, 8)(10,11);
poly := sub<Sym(12)|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,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s3*s0*s1*s2*s3*s2*s3*s2*s0*s1*s0 >;

```
References : None.
to this polytope