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

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