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

Atlas Canonical Name : {4,3,2,2,3}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 6
Schlafli Type : {4,3,2,2,3}
Number of vertices, edges, etc : 4, 6, 3, 2, 3, 3
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,2,2,3,2} of size 576
{4,3,2,2,3,3} of size 1152
{4,3,2,2,3,4} of size 1152
{4,3,2,2,3,6} of size 1728
Vertex Figure Of :
{2,4,3,2,2,3} of size 576
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,2,2,3}*576, {4,3,2,2,6}*576, {4,6,2,2,3}*576b, {4,6,2,2,3}*576c
3-fold covers : {4,3,2,2,9}*864, {4,9,2,2,3}*864, {4,3,2,6,3}*864, {4,3,6,2,3}*864
4-fold covers : {4,12,2,2,3}*1152b, {4,12,2,2,3}*1152c, {4,3,2,2,12}*1152, {4,3,2,4,6}*1152a, {4,6,4,2,3}*1152c, {8,3,2,2,3}*1152, {4,3,2,4,3}*1152b, {4,3,2,2,6}*1152, {4,6,2,2,3}*1152, {4,6,2,2,6}*1152b, {4,6,2,2,6}*1152c, {4,3,4,2,3}*1152a
5-fold covers : {4,15,2,2,3}*1440, {4,3,2,2,15}*1440
6-fold covers : {4,3,2,2,9}*1728, {4,3,2,2,18}*1728, {4,6,2,2,9}*1728b, {4,6,2,2,9}*1728c, {4,9,2,2,3}*1728, {4,9,2,2,6}*1728, {4,18,2,2,3}*1728b, {4,18,2,2,3}*1728c, {4,3,2,6,3}*1728, {4,3,2,6,6}*1728a, {4,3,2,6,6}*1728b, {4,3,6,2,3}*1728, {4,3,6,2,6}*1728, {4,6,2,6,3}*1728b, {4,6,2,6,3}*1728c, {4,6,6,2,3}*1728d, {4,6,6,2,3}*1728e, {4,6,6,2,3}*1728f, {12,3,2,2,3}*1728, {12,6,2,2,3}*1728d
Permutation Representation (GAP) :
```s0 := (1,2)(3,4);;
s1 := (2,3);;
s2 := (3,4);;
s3 := (5,6);;
s4 := (8,9);;
s5 := (7,8);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(9)!(1,2)(3,4);
s1 := Sym(9)!(2,3);
s2 := Sym(9)!(3,4);
s3 := Sym(9)!(5,6);
s4 := Sym(9)!(8,9);
s5 := Sym(9)!(7,8);
poly := sub<Sym(9)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

```

to this polytope