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# Polytope of Type {2,6,3,4}

Atlas Canonical Name : {2,6,3,4}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 5
Schlafli Type : {2,6,3,4}
Number of vertices, edges, etc : 2, 6, 9, 6, 4
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,3,4,2} of size 576
Vertex Figure Of :
{2,2,6,3,4} of size 576
{3,2,6,3,4} of size 864
{4,2,6,3,4} of size 1152
{5,2,6,3,4} of size 1440
{6,2,6,3,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,3,4}*576, {2,6,3,4}*576, {2,6,6,4}*576e, {2,6,6,4}*576f
3-fold covers : {2,6,9,4}*864, {2,6,3,4}*864, {6,6,3,4}*864b
4-fold covers : {8,6,3,4}*1152, {2,6,12,4}*1152f, {2,6,12,4}*1152g, {2,6,3,8}*1152, {4,6,3,4}*1152, {4,6,6,4}*1152g, {4,6,6,4}*1152h, {2,12,6,4}*1152e, {2,6,3,4}*1152, {2,6,6,4}*1152b, {2,12,3,4}*1152
5-fold covers : {10,6,3,4}*1440, {2,6,15,4}*1440
6-fold covers : {4,6,9,4}*1728, {4,6,3,4}*1728a, {2,6,9,4}*1728, {2,6,18,4}*1728d, {2,6,18,4}*1728e, {2,6,3,4}*1728, {2,6,6,4}*1728e, {2,6,6,4}*1728f, {12,6,3,4}*1728b, {6,6,3,4}*1728b, {6,6,6,4}*1728k, {6,6,6,4}*1728l, {2,6,3,12}*1728, {2,6,6,4}*1728i, {2,6,6,12}*1728h
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14);;
s3 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14);;
s4 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
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,
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope