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

Atlas Canonical Name : {3,2,6,4}*288a
if this polytope has a name.
Group : SmallGroup(288,958)
Rank : 5
Schlafli Type : {3,2,6,4}
Number of vertices, edges, etc : 3, 3, 6, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,6,4,2} of size 576
{3,2,6,4,4} of size 1152
{3,2,6,4,6} of size 1728
{3,2,6,4,3} of size 1728
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 : {3,2,6,2}*144
3-fold quotients : {3,2,2,4}*96
4-fold quotients : {3,2,3,2}*72
6-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,12,4}*576a, {3,2,6,8}*576, {6,2,6,4}*576a
3-fold covers : {3,2,18,4}*864a, {9,2,6,4}*864a, {3,6,6,4}*864a, {3,2,6,12}*864a, {3,2,6,12}*864c, {3,6,6,4}*864d
4-fold covers : {3,2,12,8}*1152a, {3,2,24,4}*1152a, {3,2,12,8}*1152b, {3,2,24,4}*1152b, {3,2,12,4}*1152a, {3,2,6,16}*1152, {6,2,12,4}*1152a, {6,4,6,4}*1152a, {12,2,6,4}*1152a, {6,2,6,8}*1152, {3,4,6,4}*1152a, {3,2,6,4}*1152b
5-fold covers : {3,2,6,20}*1440a, {3,2,30,4}*1440a, {15,2,6,4}*1440a
6-fold covers : {9,2,12,4}*1728a, {3,2,36,4}*1728a, {3,6,12,4}*1728a, {3,2,18,8}*1728, {9,2,6,8}*1728, {3,6,6,8}*1728a, {6,2,18,4}*1728a, {18,2,6,4}*1728a, {6,6,6,4}*1728a, {3,2,6,24}*1728a, {3,2,12,12}*1728a, {3,2,12,12}*1728c, {3,2,6,24}*1728c, {3,6,6,8}*1728b, {3,6,12,4}*1728d, {6,2,6,12}*1728a, {6,6,6,4}*1728d, {6,6,6,4}*1728e, {6,2,6,12}*1728c, {6,6,6,4}*1728i
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 9,10)(12,13)(14,15);;
s3 := ( 4, 6)( 5,12)( 8, 9)(10,13)(11,14);;
s4 := ( 4, 5)( 6, 9)( 7,10)( 8,11)(12,14)(13,15);;
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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope