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# Polytope of Type {3,6,2,14}

Atlas Canonical Name : {3,6,2,14}*1008
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 5
Schlafli Type : {3,6,2,14}
Number of vertices, edges, etc : 3, 9, 6, 14, 14
Order of s0s1s2s3s4 : 42
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) :
2-fold quotients : {3,6,2,7}*504
3-fold quotients : {3,2,2,14}*336
6-fold quotients : {3,2,2,7}*168
7-fold quotients : {3,6,2,2}*144
21-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,9)(7,8);;
s1 := (1,6)(2,4)(3,8)(5,7);;
s2 := (4,5)(6,7)(8,9);;
s3 := (12,13)(14,15)(16,17)(18,19)(20,21)(22,23);;
s4 := (10,14)(11,12)(13,18)(15,16)(17,22)(19,20)(21,23);;
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,
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*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(23)!(2,3)(4,5)(6,9)(7,8);
s1 := Sym(23)!(1,6)(2,4)(3,8)(5,7);
s2 := Sym(23)!(4,5)(6,7)(8,9);
s3 := Sym(23)!(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);
s4 := Sym(23)!(10,14)(11,12)(13,18)(15,16)(17,22)(19,20)(21,23);
poly := sub<Sym(23)|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, 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*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope