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

Atlas Canonical Name : {2,2,6,6}*432
if this polytope has a name.
Group : SmallGroup(432,545)
Rank : 5
Schlafli Type : {2,2,6,6}
Number of vertices, edges, etc : 2, 2, 9, 27, 9
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,6,6,2} of size 864
{2,2,6,6,4} of size 1728
Vertex Figure Of :
{2,2,2,6,6} of size 864
{3,2,2,6,6} of size 1296
{4,2,2,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,6,6}*864, {2,2,6,6}*864b
3-fold covers : {2,2,6,18}*1296a, {2,2,18,6}*1296a, {2,2,6,6}*1296a, {2,2,6,6}*1296b, {2,2,6,18}*1296b, {2,2,18,6}*1296b, {2,2,6,18}*1296c, {2,2,18,6}*1296c, {2,6,6,6}*1296a, {6,2,6,6}*1296
4-fold covers : {8,2,6,6}*1728, {2,2,6,12}*1728b, {2,2,12,6}*1728b, {2,4,6,6}*1728b, {4,2,6,6}*1728b, {2,2,6,12}*1728d, {2,2,12,6}*1728d, {2,4,6,6}*1728g
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 8, 9)(10,11)(12,13);;
s3 := ( 6,10)( 7, 8)( 9,11);;
s4 := ( 5, 6)( 8,13)( 9,12)(10,11);;
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*s1*s0*s1,
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*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(13)!(1,2);
s1 := Sym(13)!(3,4);
s2 := Sym(13)!( 8, 9)(10,11)(12,13);
s3 := Sym(13)!( 6,10)( 7, 8)( 9,11);
s4 := Sym(13)!( 5, 6)( 8,13)( 9,12)(10,11);
poly := sub<Sym(13)|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*s1*s0*s1, 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*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope