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

Atlas Canonical Name : {2,2,6,4,2}*384c
if this polytope has a name.
Group : SmallGroup(384,20162)
Rank : 6
Schlafli Type : {2,2,6,4,2}
Number of vertices, edges, etc : 2, 2, 6, 12, 4, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,6,4,2,2} of size 768
{2,2,6,4,2,3} of size 1152
{2,2,6,4,2,5} of size 1920
Vertex Figure Of :
{2,2,2,6,4,2} of size 768
{3,2,2,6,4,2} of size 1152
{5,2,2,6,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,3,4,2}*192
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,12,4,2}*768b, {2,2,12,4,2}*768c, {2,4,6,4,2}*768b, {4,2,6,4,2}*768c, {2,2,6,4,2}*768
3-fold covers : {2,2,18,4,2}*1152b, {2,6,6,4,2}*1152d, {2,6,6,4,2}*1152e, {6,2,6,4,2}*1152c
5-fold covers : {2,10,6,4,2}*1920b, {10,2,6,4,2}*1920c, {2,2,30,4,2}*1920b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 8)( 6,10);;
s3 := ( 5, 6)( 7, 8)( 9,10);;
s4 := ( 5, 6)( 8,10);;
s5 := (11,12);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, 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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!(1,2);
s1 := Sym(12)!(3,4);
s2 := Sym(12)!( 5, 8)( 6,10);
s3 := Sym(12)!( 5, 6)( 7, 8)( 9,10);
s4 := Sym(12)!( 5, 6)( 8,10);
s5 := Sym(12)!(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope