# Polytope of Type {2,6,4}

Atlas Canonical Name : {2,6,4}*384a
if this polytope has a name.
Group : SmallGroup(384,17948)
Rank : 4
Schlafli Type : {2,6,4}
Number of vertices, edges, etc : 2, 24, 48, 16
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,4,2} of size 768
Vertex Figure Of :
{2,2,6,4} of size 768
{3,2,6,4} of size 1152
{5,2,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {2,6,4}*96c
8-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,4}*768b, {2,12,4}*768c, {4,6,4}*768a, {2,6,8}*768b, {2,6,8}*768c, {2,6,4}*768a
3-fold covers : {2,18,4}*1152a, {6,6,4}*1152a, {6,6,4}*1152b
5-fold covers : {10,6,4}*1920a, {2,30,4}*1920a
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,11)( 4,12)( 5,13)( 6,14);;
s2 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13);;
s3 := ( 3, 5)( 4, 6)(11,13)(12,14);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope