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

Atlas Canonical Name : {2,4,6,3}*384
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 5
Schlafli Type : {2,4,6,3}
Number of vertices, edges, etc : 2, 4, 16, 12, 4
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,6,3,2} of size 768
{2,4,6,3,3} of size 1920
Vertex Figure Of :
{2,2,4,6,3} of size 768
{3,2,4,6,3} of size 1152
{5,2,4,6,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,6,3}*192
4-fold quotients : {2,2,3,3}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,6,3}*768, {2,4,12,3}*768, {2,8,6,3}*768, {2,4,6,6}*768
3-fold covers : {2,12,6,3}*1152, {6,4,6,3}*1152, {2,4,6,3}*1152a
5-fold covers : {2,20,6,3}*1920, {10,4,6,3}*1920, {2,4,6,15}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 9,10)(11,12)(13,14);;
s2 := ( 3, 9)( 4,10)( 5,13)( 6,14)( 7,11)( 8,12);;
s3 := ( 3, 5)( 4, 6)( 9,11)(10,12);;
s4 := ( 5, 8)( 6, 7)(11,14)(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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope