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# Polytope of Type {2,6,4,2}

Atlas Canonical Name : {2,6,4,2}*288
if this polytope has a name.
Group : SmallGroup(288,1031)
Rank : 5
Schlafli Type : {2,6,4,2}
Number of vertices, edges, etc : 2, 9, 18, 6, 2
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,4,2,2} of size 576
{2,6,4,2,3} of size 864
{2,6,4,2,4} of size 1152
{2,6,4,2,5} of size 1440
{2,6,4,2,6} of size 1728
Vertex Figure Of :
{2,2,6,4,2} of size 576
{3,2,6,4,2} of size 864
{4,2,6,4,2} of size 1152
{5,2,6,4,2} of size 1440
{6,2,6,4,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,6,4,4}*576, {2,6,4,2}*576
3-fold covers : {2,6,4,2}*864, {2,6,12,2}*864a, {2,6,12,2}*864b, {2,6,4,6}*864a, {2,6,12,2}*864c
4-fold covers : {2,6,4,8}*1152, {2,6,4,4}*1152, {2,12,4,2}*1152, {4,6,4,2}*1152b, {2,6,8,2}*1152
5-fold covers : {2,6,4,10}*1440, {2,6,20,2}*1440
6-fold covers : {2,6,4,4}*1728a, {2,6,12,4}*1728a, {2,6,12,4}*1728b, {2,6,4,2}*1728a, {2,6,12,2}*1728e, {2,6,12,2}*1728f, {2,6,4,12}*1728, {2,6,12,4}*1728c, {2,6,4,2}*1728b, {2,6,4,6}*1728b, {2,6,12,2}*1728h, {6,6,4,2}*1728j, {2,6,12,2}*1728i
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (4,5);;
s3 := (3,4)(5,7)(6,8);;
s4 := ( 9,10);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope