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# Polytope of Type {7,2,6,6}

Atlas Canonical Name : {7,2,6,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,11695)
Rank : 5
Schlafli Type : {7,2,6,6}
Number of vertices, edges, etc : 7, 7, 8, 24, 8
Order of s0s1s2s3s4 : 28
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 : {7,2,3,6}*672, {7,2,6,3}*672
4-fold quotients : {7,2,3,3}*336
12-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (15,16)(18,19)(20,21)(22,23);;
s3 := ( 8, 9)(10,12)(11,18)(13,15)(14,22)(16,19)(17,20)(21,23);;
s4 := ( 8,14)( 9,17)(10,11)(12,13)(15,20)(16,21)(18,22)(19,23);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope