Questions?
See the FAQ
or other info.

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

Atlas Canonical Name : {3,6,2,4}*288
if this polytope has a name.
Group : SmallGroup(288,958)
Rank : 5
Schlafli Type : {3,6,2,4}
Number of vertices, edges, etc : 3, 9, 6, 4, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,6,2,4,2} of size 576
{3,6,2,4,3} of size 864
{3,6,2,4,4} of size 1152
{3,6,2,4,6} of size 1728
{3,6,2,4,3} of size 1728
{3,6,2,4,6} of size 1728
{3,6,2,4,6} of size 1728
Vertex Figure Of :
{2,3,6,2,4} of size 576
{4,3,6,2,4} of size 1152
{6,3,6,2,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,6,2,2}*144
3-fold quotients : {3,2,2,4}*96
6-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,6,2,8}*576, {3,6,4,4}*576, {6,6,2,4}*576c
3-fold covers : {9,6,2,4}*864, {3,6,2,4}*864, {3,6,2,12}*864, {3,6,6,4}*864d
4-fold covers : {3,6,4,8}*1152a, {3,6,8,4}*1152a, {3,6,4,8}*1152b, {3,6,8,4}*1152b, {3,6,4,4}*1152, {3,6,2,16}*1152, {6,6,4,4}*1152c, {6,12,2,4}*1152a, {12,6,2,4}*1152c, {6,6,2,8}*1152c, {3,6,2,4}*1152, {3,12,2,4}*1152
5-fold covers : {3,6,2,20}*1440, {3,6,10,4}*1440, {15,6,2,4}*1440
6-fold covers : {9,6,2,8}*1728, {3,6,2,8}*1728, {9,6,4,4}*1728, {3,6,4,4}*1728a, {18,6,2,4}*1728b, {6,6,2,4}*1728c, {3,6,2,24}*1728, {3,6,4,12}*1728, {3,6,6,8}*1728b, {3,6,12,4}*1728d, {6,6,2,12}*1728c, {6,6,2,4}*1728d, {6,6,6,4}*1728i
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,9)(7,8);;
s1 := (1,6)(2,4)(3,8)(5,7);;
s2 := (4,5)(6,7)(8,9);;
s3 := (11,12);;
s4 := (10,11)(12,13);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*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*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```

to this polytope