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# Polytope of Type {3,2,12,4}

Atlas Canonical Name : {3,2,12,4}*1296
if this polytope has a name.
Group : SmallGroup(1296,2909)
Rank : 5
Schlafli Type : {3,2,12,4}
Number of vertices, edges, etc : 3, 3, 27, 54, 9
Order of s0s1s2s3s4 : 6
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 : {3,2,4,4}*432
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 8, 9)(11,12)(14,15)(16,19)(17,21)(18,20);;
s3 := ( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18)(10,20)(11,19)(12,21);;
s4 := ( 4, 7)( 5, 9)( 6, 8)(11,12)(14,15)(16,17)(19,21);;
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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(21)!(2,3);
s1 := Sym(21)!(1,2);
s2 := Sym(21)!( 5, 6)( 8, 9)(11,12)(14,15)(16,19)(17,21)(18,20);
s3 := Sym(21)!( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18)(10,20)(11,19)(12,21);
s4 := Sym(21)!( 4, 7)( 5, 9)( 6, 8)(11,12)(14,15)(16,17)(19,21);
poly := sub<Sym(21)|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*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope