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# Polytope of Type {3,2,2,2,6}

Atlas Canonical Name : {3,2,2,2,6}*288
if this polytope has a name.
Group : SmallGroup(288,1040)
Rank : 6
Schlafli Type : {3,2,2,2,6}
Number of vertices, edges, etc : 3, 3, 2, 2, 6, 6
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,2,2,6,2} of size 576
{3,2,2,2,6,3} of size 864
{3,2,2,2,6,4} of size 1152
{3,2,2,2,6,3} of size 1152
{3,2,2,2,6,4} of size 1152
{3,2,2,2,6,4} of size 1152
{3,2,2,2,6,4} of size 1728
{3,2,2,2,6,6} of size 1728
{3,2,2,2,6,6} of size 1728
{3,2,2,2,6,6} of size 1728
Vertex Figure Of :
{2,3,2,2,2,6} of size 576
{3,3,2,2,2,6} of size 1152
{4,3,2,2,2,6} of size 1152
{6,3,2,2,2,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2,2,3}*144
3-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,2,2,12}*576, {3,2,2,4,6}*576a, {3,2,4,2,6}*576, {6,2,2,2,6}*576
3-fold covers : {3,2,2,2,18}*864, {9,2,2,2,6}*864, {3,2,2,6,6}*864a, {3,2,2,6,6}*864b, {3,2,6,2,6}*864, {3,6,2,2,6}*864
4-fold covers : {3,2,4,4,6}*1152, {3,2,2,4,12}*1152a, {3,2,4,2,12}*1152, {3,2,2,8,6}*1152, {3,2,8,2,6}*1152, {3,2,2,2,24}*1152, {6,2,2,4,6}*1152a, {6,2,4,2,6}*1152, {6,4,2,2,6}*1152a, {6,2,2,2,12}*1152, {12,2,2,2,6}*1152, {3,2,2,4,6}*1152, {3,4,2,2,6}*1152
5-fold covers : {3,2,2,10,6}*1440, {3,2,10,2,6}*1440, {3,2,2,2,30}*1440, {15,2,2,2,6}*1440
6-fold covers : {9,2,2,2,12}*1728, {3,2,2,2,36}*1728, {3,2,2,4,18}*1728a, {3,2,4,2,18}*1728, {9,2,2,4,6}*1728a, {9,2,4,2,6}*1728, {6,2,2,2,18}*1728, {18,2,2,2,6}*1728, {3,2,2,6,12}*1728a, {3,2,2,6,12}*1728b, {3,2,2,12,6}*1728a, {3,2,6,2,12}*1728, {3,2,12,2,6}*1728, {3,6,2,2,12}*1728, {3,2,4,6,6}*1728a, {3,2,6,4,6}*1728, {3,6,2,4,6}*1728a, {3,2,2,12,6}*1728c, {3,2,4,6,6}*1728c, {3,6,4,2,6}*1728, {6,2,2,6,6}*1728a, {6,2,2,6,6}*1728b, {6,2,6,2,6}*1728, {6,6,2,2,6}*1728a, {6,6,2,2,6}*1728c
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := (6,7);;
s4 := (10,11)(12,13);;
s5 := ( 8,12)( 9,10)(11,13);;
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*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, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2);
s2 := Sym(13)!(4,5);
s3 := Sym(13)!(6,7);
s4 := Sym(13)!(10,11)(12,13);
s5 := Sym(13)!( 8,12)( 9,10)(11,13);
poly := sub<Sym(13)|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*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,
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

```

to this polytope