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# Polytope of Type {6,6}

Atlas Canonical Name : {6,6}*576e
if this polytope has a name.
Group : SmallGroup(576,8654)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 48, 144, 48
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{6,6,2} of size 1152
Vertex Figure Of :
{2,6,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
16-fold quotients : {3,6}*36
48-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,6}*1152h, {12,6}*1152i, {6,6}*1152i
3-fold covers : {18,6}*1728b, {6,6}*1728c
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);;
s1 := ( 1, 7)( 2, 8)( 3, 6)( 4, 5)( 9,10);;
s2 := ( 2, 3)( 7, 8)(10,12);;
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*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope