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# Polytope of Type {2,2,3,6,4}

Atlas Canonical Name : {2,2,3,6,4}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 6
Schlafli Type : {2,2,3,6,4}
Number of vertices, edges, etc : 2, 2, 3, 27, 36, 12
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
9-fold quotients : {2,2,3,2,4}*192
18-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21);;
s3 := ( 5,12)( 6,11)( 7,13)( 8, 9)(14,18)(15,17)(16,19)(20,21);;
s4 := ( 8,11)( 9,12)(10,13);;
s5 := ( 5,14)( 6,15)( 7,16)( 8,20)( 9,21)(10,22)(11,17)(12,18)(13,19);;
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*s1*s0*s1, 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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(22)!(1,2);
s1 := Sym(22)!(3,4);
s2 := Sym(22)!( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21);
s3 := Sym(22)!( 5,12)( 6,11)( 7,13)( 8, 9)(14,18)(15,17)(16,19)(20,21);
s4 := Sym(22)!( 8,11)( 9,12)(10,13);
s5 := Sym(22)!( 5,14)( 6,15)( 7,16)( 8,20)( 9,21)(10,22)(11,17)(12,18)(13,19);
poly := sub<Sym(22)|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*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4 >;

```

to this polytope