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# Polytope of Type {6,10,6}

Atlas Canonical Name : {6,10,6}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5853)
Rank : 4
Schlafli Type : {6,10,6}
Number of vertices, edges, etc : 6, 60, 60, 12
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {6,10,3}*720
3-fold quotients : {2,10,6}*480d
6-fold quotients : {2,5,6}*240c, {2,10,3}*240a
12-fold quotients : {2,5,3}*120
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (12,16)(13,15);;
s1 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,12)(13,16)(14,15);;
s2 := (1,3)(2,4)(5,8)(6,7);;
s3 := ( 1, 2)( 3, 9)( 4,10)( 5, 7)( 6, 8);;
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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s3*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;

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

```
References : None.
to this polytope