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

Atlas Canonical Name : {2,6,6,2}*288c
if this polytope has a name.
Group : SmallGroup(288,1040)
Rank : 5
Schlafli Type : {2,6,6,2}
Number of vertices, edges, etc : 2, 6, 18, 6, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,6,2,2} of size 576
{2,6,6,2,3} of size 864
{2,6,6,2,4} of size 1152
{2,6,6,2,5} of size 1440
{2,6,6,2,6} of size 1728
Vertex Figure Of :
{2,2,6,6,2} of size 576
{3,2,6,6,2} of size 864
{4,2,6,6,2} of size 1152
{5,2,6,6,2} of size 1440
{6,2,6,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,6,2}*144
3-fold quotients : {2,6,2,2}*96
6-fold quotients : {2,3,2,2}*48
9-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,6,2}*576b, {4,6,6,2}*576b, {2,6,6,4}*576c, {2,6,12,2}*576c
3-fold covers : {2,18,6,2}*864b, {2,6,6,2}*864c, {2,6,6,2}*864d, {2,6,6,6}*864g, {6,6,6,2}*864e, {6,6,6,2}*864f
4-fold covers : {4,12,6,2}*1152b, {2,6,12,4}*1152c, {2,12,12,2}*1152c, {4,6,6,4}*1152b, {4,6,12,2}*1152a, {2,12,6,4}*1152c, {8,6,6,2}*1152b, {2,6,6,8}*1152c, {2,6,24,2}*1152a, {2,24,6,2}*1152c, {2,6,6,2}*1152b, {2,6,12,2}*1152b, {4,6,6,2}*1152b
5-fold covers : {2,6,6,10}*1440c, {2,6,30,2}*1440a, {10,6,6,2}*1440c, {2,30,6,2}*1440c
6-fold covers : {2,36,6,2}*1728b, {2,12,6,2}*1728a, {4,18,6,2}*1728b, {4,6,6,2}*1728a, {2,18,6,4}*1728b, {2,18,12,2}*1728b, {2,6,6,4}*1728c, {2,6,12,2}*1728c, {2,12,6,6}*1728d, {6,12,6,2}*1728d, {6,12,6,2}*1728e, {12,6,6,2}*1728c, {4,6,6,6}*1728f, {2,6,6,12}*1728e, {2,6,12,2}*1728g, {2,12,6,2}*1728g, {6,6,6,4}*1728g, {6,6,6,4}*1728h, {2,6,6,4}*1728h, {2,6,12,6}*1728f, {4,6,6,2}*1728h, {6,6,12,2}*1728f, {6,6,12,2}*1728g, {12,6,6,2}*1728g
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,20)(18,19);;
s2 := ( 3,17)( 4,13)( 5,11)( 6,19)( 7, 9)( 8,18)(10,15)(12,14)(16,20);;
s3 := ( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20);;
s4 := (21,22);;
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope