# Polytope of Type {4,8,2,5}

Atlas Canonical Name : {4,8,2,5}*640b
if this polytope has a name.
Group : SmallGroup(640,14089)
Rank : 5
Schlafli Type : {4,8,2,5}
Number of vertices, edges, etc : 4, 16, 8, 5, 5
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,8,2,5,2} of size 1280
Vertex Figure Of :
{2,4,8,2,5} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4,2,5}*320
4-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160
8-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,8,2,5}*1280a, {8,8,2,5}*1280c, {8,8,2,5}*1280d, {4,8,2,10}*1280b
3-fold covers : {4,8,2,15}*1920b, {12,8,2,5}*1920b, {4,24,2,5}*1920b
Permutation Representation (GAP) :
```s0 := ( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);;
s2 := ( 2, 3)( 4, 6)( 5, 8)( 7,10)(11,14)(13,15);;
s3 := (18,19)(20,21);;
s4 := (17,18)(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*s2*s0*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*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(21)!( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);
s1 := Sym(21)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);
s2 := Sym(21)!( 2, 3)( 4, 6)( 5, 8)( 7,10)(11,14)(13,15);
s3 := Sym(21)!(18,19)(20,21);
s4 := Sym(21)!(17,18)(19,20);
poly := sub<Sym(21)|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*s2*s0*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*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope