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# Polytope of Type {9,2,6,2}

Atlas Canonical Name : {9,2,6,2}*432
if this polytope has a name.
Group : SmallGroup(432,544)
Rank : 5
Schlafli Type : {9,2,6,2}
Number of vertices, edges, etc : 9, 9, 6, 6, 2
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{9,2,6,2,2} of size 864
{9,2,6,2,3} of size 1296
{9,2,6,2,4} of size 1728
Vertex Figure Of :
{2,9,2,6,2} of size 864
{4,9,2,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {9,2,3,2}*216
3-fold quotients : {9,2,2,2}*144, {3,2,6,2}*144
6-fold quotients : {3,2,3,2}*72
9-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {9,2,12,2}*864, {9,2,6,4}*864a, {18,2,6,2}*864
3-fold covers : {9,2,18,2}*1296, {9,6,6,2}*1296a, {27,2,6,2}*1296, {9,2,6,6}*1296a, {9,2,6,6}*1296c, {9,6,6,2}*1296b
4-fold covers : {9,2,12,4}*1728a, {9,2,24,2}*1728, {9,2,6,8}*1728, {18,2,12,2}*1728, {36,2,6,2}*1728, {18,2,6,4}*1728a, {18,4,6,2}*1728, {9,2,6,4}*1728, {9,4,6,2}*1728
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,13)(14,15);;
s3 := (10,14)(11,12)(13,15);;
s4 := (16,17);;
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,
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(17)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(17)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(17)!(12,13)(14,15);
s3 := Sym(17)!(10,14)(11,12)(13,15);
s4 := Sym(17)!(16,17);
poly := sub<Sym(17)|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, s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope