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# Polytope of Type {3,4,6}

Atlas Canonical Name : {3,4,6}*720
if this polytope has a name.
Group : SmallGroup(720,767)
Rank : 4
Schlafli Type : {3,4,6}
Number of vertices, edges, etc : 3, 30, 60, 30
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 6
Special Properties :
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,4,6,2} of size 1440
Vertex Figure Of :
{2,3,4,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,4,6}*1440d
Permutation Representation (GAP) :
```s0 := (2,3)(7,8);;
s1 := (1,2)(6,7);;
s2 := (5,6)(7,8);;
s3 := (4,5);;
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, s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s0*s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s2*s3*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(8)!(2,3)(7,8);
s1 := Sym(8)!(1,2)(6,7);
s2 := Sym(8)!(5,6)(7,8);
s3 := Sym(8)!(4,5);
poly := sub<Sym(8)|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,
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s0*s2*s1*s0*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s0*s2*s3*s2*s1*s3*s2*s3*s1*s2*s3*s2*s3*s0*s1*s2*s1 >;

```
References : None.
to this polytope