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

Atlas Canonical Name : {6,2,2,2,2,2}*384
if this polytope has a name.
Group : SmallGroup(384,20168)
Rank : 7
Schlafli Type : {6,2,2,2,2,2}
Number of vertices, edges, etc : 6, 6, 2, 2, 2, 2, 2
Order of s0s1s2s3s4s5s6 : 6
Order of s0s1s2s3s4s5s6s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,2,2,2,2,2} of size 768
{6,2,2,2,2,2,3} of size 1152
{6,2,2,2,2,2,5} of size 1920
Vertex Figure Of :
{2,6,2,2,2,2,2} of size 768
{3,6,2,2,2,2,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2,2,2,2}*192
3-fold quotients : {2,2,2,2,2,2}*128
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,2,2,2,2,4}*768, {6,2,2,2,4,2}*768, {6,2,2,4,2,2}*768, {6,2,4,2,2,2}*768, {6,4,2,2,2,2}*768a, {12,2,2,2,2,2}*768
3-fold covers : {18,2,2,2,2,2}*1152, {6,2,2,2,2,6}*1152, {6,2,2,2,6,2}*1152, {6,2,2,6,2,2}*1152, {6,2,6,2,2,2}*1152, {6,6,2,2,2,2}*1152a, {6,6,2,2,2,2}*1152c
5-fold covers : {30,2,2,2,2,2}*1920, {6,2,2,2,2,10}*1920, {6,2,2,2,10,2}*1920, {6,2,2,10,2,2}*1920, {6,2,10,2,2,2}*1920, {6,10,2,2,2,2}*1920
Permutation Representation (GAP) :
```s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
s3 := ( 9,10);;
s4 := (11,12);;
s5 := (13,14);;
s6 := (15,16);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s6*s6, s0*s2*s0*s2, s1*s2*s1*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, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6,
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6,
s4*s6*s4*s6, s5*s6*s5*s6, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(16)!(3,4)(5,6);
s1 := Sym(16)!(1,5)(2,3)(4,6);
s2 := Sym(16)!(7,8);
s3 := Sym(16)!( 9,10);
s4 := Sym(16)!(11,12);
s5 := Sym(16)!(13,14);
s6 := Sym(16)!(15,16);
poly := sub<Sym(16)|s0,s1,s2,s3,s4,s5,s6>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s6*s6, s0*s2*s0*s2,
s1*s2*s1*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, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s0*s6*s0*s6, s1*s6*s1*s6,
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6,
s5*s6*s5*s6, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope