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# Polytope of Type {2,8,4,2}

Atlas Canonical Name : {2,8,4,2}*512b
if this polytope has a name.
Group : SmallGroup(512,7530050)
Rank : 5
Schlafli Type : {2,8,4,2}
Number of vertices, edges, etc : 2, 16, 32, 8, 2
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,4,4,2}*256
4-fold quotients : {2,4,4,2}*128
8-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
16-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,11)( 4,12)( 5,13)( 6,14)( 7,17)( 8,18)( 9,15)(10,16);;
s2 := ( 5, 6)( 9,10)(11,15)(12,16)(13,18)(14,17);;
s3 := ( 7, 9)( 8,10)(15,17)(16,18);;
s4 := (19,20);;
poly := Group([s0,s1,s2,s3,s4]);;

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

```
Permutation Representation (Magma) :
```s0 := Sym(20)!(1,2);
s1 := Sym(20)!( 3,11)( 4,12)( 5,13)( 6,14)( 7,17)( 8,18)( 9,15)(10,16);
s2 := Sym(20)!( 5, 6)( 9,10)(11,15)(12,16)(13,18)(14,17);
s3 := Sym(20)!( 7, 9)( 8,10)(15,17)(16,18);
s4 := Sym(20)!(19,20);
poly := sub<Sym(20)|s0,s1,s2,s3,s4>;

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

```

to this polytope