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# Polytope of Type {6,40,2}

Atlas Canonical Name : {6,40,2}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240561)
Rank : 4
Schlafli Type : {6,40,2}
Number of vertices, edges, etc : 12, 240, 80, 2
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 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 : {6,20,2}*960a
4-fold quotients : {6,10,2}*480c
8-fold quotients : {3,10,2}*240b, {6,5,2}*240c
16-fold quotients : {3,5,2}*120
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (10,11)(12,13);;
s1 := ( 2, 4)( 3, 6)( 5, 8)( 9,10)(12,13);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)(10,12)(11,13);;
s3 := (14,15);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(15)!(10,11)(12,13);
s1 := Sym(15)!( 2, 4)( 3, 6)( 5, 8)( 9,10)(12,13);
s2 := Sym(15)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)(10,12)(11,13);
s3 := Sym(15)!(14,15);
poly := sub<Sym(15)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1 >;

```

to this polytope