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# Polytope of Type {2,3,2,12}

Atlas Canonical Name : {2,3,2,12}*288
if this polytope has a name.
Group : SmallGroup(288,951)
Rank : 5
Schlafli Type : {2,3,2,12}
Number of vertices, edges, etc : 2, 3, 3, 12, 12
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,2,12,2} of size 576
{2,3,2,12,4} of size 1152
{2,3,2,12,4} of size 1152
{2,3,2,12,4} of size 1152
{2,3,2,12,3} of size 1152
{2,3,2,12,6} of size 1728
{2,3,2,12,6} of size 1728
{2,3,2,12,6} of size 1728
{2,3,2,12,3} of size 1728
{2,3,2,12,6} of size 1728
Vertex Figure Of :
{2,2,3,2,12} of size 576
{3,2,3,2,12} of size 864
{4,2,3,2,12} of size 1152
{5,2,3,2,12} of size 1440
{6,2,3,2,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,2,6}*144
3-fold quotients : {2,3,2,4}*96
4-fold quotients : {2,3,2,3}*72
6-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,3,2,24}*576, {2,6,2,12}*576
3-fold covers : {2,3,2,36}*864, {2,9,2,12}*864, {2,3,6,12}*864a, {6,3,2,12}*864, {2,3,6,12}*864b
4-fold covers : {2,3,2,48}*1152, {2,6,4,12}*1152, {4,6,2,12}*1152a, {2,12,2,12}*1152, {2,6,2,24}*1152, {2,3,4,12}*1152, {4,3,2,12}*1152
5-fold covers : {2,15,2,12}*1440, {2,3,2,60}*1440
6-fold covers : {2,3,2,72}*1728, {2,9,2,24}*1728, {2,3,6,24}*1728a, {2,18,2,12}*1728, {2,6,2,36}*1728, {2,6,6,12}*1728a, {6,3,2,24}*1728, {2,3,6,24}*1728b, {2,6,6,12}*1728b, {2,6,6,12}*1728c, {6,6,2,12}*1728a, {6,6,2,12}*1728b, {2,6,6,12}*1728e
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := ( 7, 8)( 9,10)(12,15)(13,14)(16,17);;
s4 := ( 6,12)( 7, 9)( 8,16)(10,13)(11,14)(15,17);;
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,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(17)!(1,2);
s1 := Sym(17)!(4,5);
s2 := Sym(17)!(3,4);
s3 := Sym(17)!( 7, 8)( 9,10)(12,15)(13,14)(16,17);
s4 := Sym(17)!( 6,12)( 7, 9)( 8,16)(10,13)(11,14)(15,17);
poly := sub<Sym(17)|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, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope