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# Polytope of Type {9,6,2}

Atlas Canonical Name : {9,6,2}*648b
if this polytope has a name.
Group : SmallGroup(648,299)
Rank : 4
Schlafli Type : {9,6,2}
Number of vertices, edges, etc : 27, 81, 18, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{9,6,2,2} of size 1296
{9,6,2,3} of size 1944
Vertex Figure Of :
{2,9,6,2} of size 1296
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,6,2}*216
9-fold quotients : {3,6,2}*72
27-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {9,6,4}*1296c, {18,6,2}*1296d
3-fold covers : {9,6,2}*1944a, {9,6,2}*1944b, {9,6,2}*1944c, {9,6,2}*1944d, {9,18,2}*1944j, {9,6,6}*1944g
Permutation Representation (GAP) :
```s0 := (1,7)(2,9)(3,8)(5,6);;
s1 := (2,3)(4,8)(5,7)(6,9);;
s2 := (2,3)(5,6)(8,9);;
s3 := (10,11);;
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, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope