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

Atlas Canonical Name : {2,2,2,6,6}*576b
if this polytope has a name.
Group : SmallGroup(576,8675)
Rank : 6
Schlafli Type : {2,2,2,6,6}
Number of vertices, edges, etc : 2, 2, 2, 6, 18, 6
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,6,6,2} of size 1152
Vertex Figure Of :
{2,2,2,2,6,6} of size 1152
{3,2,2,2,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,6,3}*288
3-fold quotients : {2,2,2,2,6}*192
6-fold quotients : {2,2,2,2,3}*96
9-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,2,6,6}*1152b, {4,2,2,6,6}*1152b, {2,2,2,12,6}*1152a, {2,2,4,6,6}*1152c, {2,2,2,6,12}*1152c
3-fold covers : {2,2,2,6,18}*1728b, {2,2,2,6,6}*1728a, {2,2,2,6,6}*1728d, {2,2,6,6,6}*1728c, {2,6,2,6,6}*1728b, {6,2,2,6,6}*1728b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (11,12)(15,16)(17,18)(19,20)(21,22)(23,24);;
s4 := ( 7,11)( 8,15)( 9,19)(10,17)(13,23)(14,21)(18,20)(22,24);;
s5 := ( 7,13)( 8, 9)(10,14)(11,22)(12,21)(15,18)(16,17)(19,24)(20,23);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(24)!(1,2);
s1 := Sym(24)!(3,4);
s2 := Sym(24)!(5,6);
s3 := Sym(24)!(11,12)(15,16)(17,18)(19,20)(21,22)(23,24);
s4 := Sym(24)!( 7,11)( 8,15)( 9,19)(10,17)(13,23)(14,21)(18,20)(22,24);
s5 := Sym(24)!( 7,13)( 8, 9)(10,14)(11,22)(12,21)(15,18)(16,17)(19,24)(20,23);
poly := sub<Sym(24)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

```

to this polytope