Questions?
See the FAQ
or other info.

# Polytope of Type {8,4,2}

Atlas Canonical Name : {8,4,2}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11684)
Rank : 4
Schlafli Type : {8,4,2}
Number of vertices, edges, etc : 84, 168, 42, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,4,2}*672a
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (3,7)(4,8)(5,6);;
s1 := ( 1, 3)( 2, 6)( 4, 7)( 5, 8)( 9,10);;
s2 := (1,2)(3,4)(5,6)(7,8);;
s3 := (11,12);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope