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# Polytope of Type {2,3,12}

Atlas Canonical Name : {2,3,12}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 4
Schlafli Type : {2,3,12}
Number of vertices, edges, etc : 2, 6, 36, 24
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,12,2} of size 576
{2,3,12,4} of size 1152
{2,3,12,6} of size 1728
{2,3,12,6} of size 1728
Vertex Figure Of :
{2,2,3,12} of size 576
{3,2,3,12} of size 864
{4,2,3,12} of size 1152
{5,2,3,12} of size 1440
{6,2,3,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,3,4}*96
4-fold quotients : {2,3,6}*72
6-fold quotients : {2,3,4}*48
12-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,3,24}*576, {2,6,12}*576b
3-fold covers : {2,9,12}*864, {2,3,12}*864, {6,3,12}*864
4-fold covers : {2,3,24}*1152, {2,12,12}*1152e, {2,12,12}*1152h, {4,6,12}*1152c, {2,6,24}*1152b, {2,6,24}*1152d, {2,6,12}*1152f, {2,3,12}*1152, {4,3,12}*1152b
5-fold covers : {2,15,12}*1440
6-fold covers : {2,9,24}*1728, {2,3,24}*1728, {2,18,12}*1728b, {2,6,12}*1728a, {6,3,24}*1728, {6,6,12}*1728c, {6,6,12}*1728d, {2,6,12}*1728c
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13);;
s3 := ( 3, 4)( 5, 6)( 7,12)( 8,11)( 9,14)(10,13);;
poly := Group([s0,s1,s2,s3]);;

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

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

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

```

to this polytope