# Polytope of Type {8,2,2,5,2}

Atlas Canonical Name : {8,2,2,5,2}*640
if this polytope has a name.
Group : SmallGroup(640,21152)
Rank : 6
Schlafli Type : {8,2,2,5,2}
Number of vertices, edges, etc : 8, 8, 2, 5, 5, 2
Order of s0s1s2s3s4s5 : 40
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,2,2,5,2,2} of size 1280
{8,2,2,5,2,3} of size 1920
Vertex Figure Of :
{2,8,2,2,5,2} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,2,2,5,2}*320
4-fold quotients : {2,2,2,5,2}*160
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,4,2,5,2}*1280a, {16,2,2,5,2}*1280, {8,2,2,10,2}*1280
3-fold covers : {8,2,2,15,2}*1920, {8,6,2,5,2}*1920, {24,2,2,5,2}*1920
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := ( 9,10);;
s3 := (12,13)(14,15);;
s4 := (11,12)(13,14);;
s5 := (16,17);;
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*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, 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*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(17)!(2,3)(4,5)(6,7);
s1 := Sym(17)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(17)!( 9,10);
s3 := Sym(17)!(12,13)(14,15);
s4 := Sym(17)!(11,12)(13,14);
s5 := Sym(17)!(16,17);
poly := sub<Sym(17)|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*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,
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*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope