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

Atlas Canonical Name : {3,4,4,3,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,157852)
Rank : 6
Schlafli Type : {3,4,4,3,2}
Number of vertices, edges, etc : 3, 12, 16, 12, 3, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 7, 8)(10,12);;
s1 := ( 2, 4)( 6, 7)(11,12);;
s2 := (1,4)(2,3)(5,6)(7,8);;
s3 := ( 5, 9)( 6,11)( 7,12)( 8,10);;
s4 := (1,5)(2,7)(3,8)(4,6);;
s5 := (13,14);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s0*s2*s1*s0*s2*s1,
s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(14)!( 2, 3)( 7, 8)(10,12);
s1 := Sym(14)!( 2, 4)( 6, 7)(11,12);
s2 := Sym(14)!(1,4)(2,3)(5,6)(7,8);
s3 := Sym(14)!( 5, 9)( 6,11)( 7,12)( 8,10);
s4 := Sym(14)!(1,5)(2,7)(3,8)(4,6);
s5 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s0*s2*s1*s0*s2*s1, s4*s2*s3*s4*s2*s3*s4*s2*s3 >;

```

to this polytope