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# Polytope of Type {5,6}

Atlas Canonical Name : {5,6}*660
if this polytope has a name.
Group : SmallGroup(660,13)
Rank : 3
Schlafli Type : {5,6}
Number of vertices, edges, etc : 55, 165, 66
Order of s0s1s2 : 6
Order of s0s1s2s1 : 5
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{5,6,2} of size 1320
Vertex Figure Of :
{2,5,6} of size 1320
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,6}*1320b, {5,6}*1320c, {5,6}*1320d, {10,6}*1320c, {10,6}*1320d, {10,6}*1320e, {10,6}*1320f
Permutation Representation (GAP) :
```s0 := ( 3,11)( 4, 7)( 5, 6)( 8,10);;
s1 := ( 2, 5)( 3, 6)( 4,10)( 8, 9);;
s2 := ( 1, 2)( 3, 4)( 7,11)( 8,10);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope