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# Polytope of Type {5,2,2,18,2}

Atlas Canonical Name : {5,2,2,18,2}*1440
if this polytope has a name.
Group : SmallGroup(1440,4583)
Rank : 6
Schlafli Type : {5,2,2,18,2}
Number of vertices, edges, etc : 5, 5, 2, 18, 18, 2
Order of s0s1s2s3s4s5 : 90
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) :
2-fold quotients : {5,2,2,9,2}*720
3-fold quotients : {5,2,2,6,2}*480
6-fold quotients : {5,2,2,3,2}*240
9-fold quotients : {5,2,2,2,2}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := (10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);;
s4 := ( 8,12)( 9,10)(11,16)(13,14)(15,20)(17,18)(19,24)(21,22)(23,25);;
s5 := (26,27);;
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, s1*s2*s1*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,
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(27)!(2,3)(4,5);
s1 := Sym(27)!(1,2)(3,4);
s2 := Sym(27)!(6,7);
s3 := Sym(27)!(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);
s4 := Sym(27)!( 8,12)( 9,10)(11,16)(13,14)(15,20)(17,18)(19,24)(21,22)(23,25);
s5 := Sym(27)!(26,27);
poly := sub<Sym(27)|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, s1*s2*s1*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, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope