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

Atlas Canonical Name : {3,2,6,4}*288b
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 5
Schlafli Type : {3,2,6,4}
Number of vertices, edges, etc : 3, 3, 6, 12, 4
Order of s0s1s2s3s4 : 3
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,6,4,2} of size 576
Vertex Figure Of :
{2,3,2,6,4} of size 576
{3,3,2,6,4} of size 1152
{4,3,2,6,4} of size 1152
{6,3,2,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,3,4}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,6,4}*576, {6,2,6,4}*576b
3-fold covers : {9,2,6,4}*864b, {3,2,18,4}*864c, {3,6,6,4}*864c, {3,2,6,12}*864d
4-fold covers : {3,2,6,8}*1152a, {3,2,12,4}*1152b, {12,2,6,4}*1152b, {3,2,6,4}*1152b, {3,2,12,4}*1152c, {3,2,6,8}*1152b, {3,2,6,8}*1152c, {6,2,6,4}*1152
5-fold covers : {3,2,6,20}*1440b, {3,2,30,4}*1440c, {15,2,6,4}*1440b
6-fold covers : {9,2,6,4}*1728, {18,2,6,4}*1728b, {3,2,18,4}*1728, {6,2,18,4}*1728c, {3,6,6,4}*1728a, {6,6,6,4}*1728c, {3,6,6,4}*1728b, {6,6,6,4}*1728l, {3,2,6,12}*1728a, {3,2,6,12}*1728b, {6,2,6,12}*1728d
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (4,7)(5,9);;
s3 := (4,5)(6,7)(8,9);;
s4 := (6,8);;
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*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,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s2*s3*s4*s2*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope