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# Polytope of Type {6,2,5,5}

Atlas Canonical Name : {6,2,5,5}*720
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 5
Schlafli Type : {6,2,5,5}
Number of vertices, edges, etc : 6, 6, 6, 15, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,5,5,2} of size 1440
Vertex Figure Of :
{2,6,2,5,5} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,5,5}*360
3-fold quotients : {2,2,5,5}*240
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,5,5}*1440, {6,2,5,5}*1440, {6,2,5,10}*1440a, {6,2,5,10}*1440b, {6,2,10,5}*1440a, {6,2,10,5}*1440b
Permutation Representation (GAP) :
```s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11);;
s3 := ( 7, 8)( 9,10);;
s4 := ( 8,10)( 9,11);;
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,
s2*s3*s4*s2*s3*s4*s2*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!(3,4)(5,6);
s1 := Sym(11)!(1,5)(2,3)(4,6);
s2 := Sym(11)!( 8, 9)(10,11);
s3 := Sym(11)!( 7, 8)( 9,10);
s4 := Sym(11)!( 8,10)( 9,11);
poly := sub<Sym(11)|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, s2*s3*s4*s2*s3*s4*s2*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope