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

Atlas Canonical Name : {6,6,2,3,4}*1728c
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 6
Schlafli Type : {6,6,2,3,4}
Number of vertices, edges, etc : 6, 18, 6, 3, 6, 4
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) :
2-fold quotients : {3,6,2,3,4}*864
3-fold quotients : {6,2,2,3,4}*576
6-fold quotients : {3,2,2,3,4}*288
9-fold quotients : {2,2,2,3,4}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,18)(16,17);;
s1 := ( 1,15)( 2,11)( 3, 9)( 4,17)( 5, 7)( 6,16)( 8,13)(10,12)(14,18);;
s2 := ( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s3 := (21,22);;
s4 := (20,21);;
s5 := (19,20)(21,22);;
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,
s2*s3*s2*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, s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s3*s5*s4*s3*s5*s4*s3*s5*s4,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope