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# Polytope of Type {4,2,4,6}

Atlas Canonical Name : {4,2,4,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,30394)
Rank : 5
Schlafli Type : {4,2,4,6}
Number of vertices, edges, etc : 4, 4, 18, 54, 27
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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) :
2-fold quotients : {2,2,4,6}*864
3-fold quotients : {4,2,4,6}*576
6-fold quotients : {2,2,4,6}*288
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(17,20)(18,22)(19,21);;
s3 := ( 5,14)( 6,16)( 7,15)( 8,17)( 9,19)(10,18)(11,20)(12,22)(13,21);;
s4 := ( 5, 8)( 6, 9)( 7,10)(17,22)(18,20)(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*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(22)!(2,3);
s1 := Sym(22)!(1,2)(3,4);
s2 := Sym(22)!( 6, 7)( 9,10)(12,13)(15,16)(17,20)(18,22)(19,21);
s3 := Sym(22)!( 5,14)( 6,16)( 7,15)( 8,17)( 9,19)(10,18)(11,20)(12,22)(13,21);
s4 := Sym(22)!( 5, 8)( 6, 9)( 7,10)(17,22)(18,20)(19,21);
poly := sub<Sym(22)|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*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3*s2 >;

```

to this polytope