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# Polytope of Type {2,8,6}

Atlas Canonical Name : {2,8,6}*384a
if this polytope has a name.
Group : SmallGroup(384,17949)
Rank : 4
Schlafli Type : {2,8,6}
Number of vertices, edges, etc : 2, 16, 48, 12
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,8,6,2} of size 768
Vertex Figure Of :
{2,2,8,6} of size 768
{3,2,8,6} of size 1152
{5,2,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {2,4,6}*96b
8-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,8,12}*768c, {2,8,12}*768d, {2,8,6}*768d
3-fold covers : {2,8,18}*1152a, {2,24,6}*1152a
5-fold covers : {2,40,6}*1920a, {2,8,30}*1920a
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 7, 9)( 8,10)(11,13)(12,14);;
s2 := ( 3, 7)( 4, 8)( 5, 9)( 6,10)(13,14);;
s3 := ( 7,13)( 8,14)( 9,11)(10,12);;
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,
s1*s2*s3*s1*s2*s3*s1*s2*s3, s2*s3*s2*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 ];;
poly := F / rels;;

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

```

to this polytope