# Polytope of Type {8,6,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,5}*960a
if this polytope has a name.
Group : SmallGroup(960,5713)
Rank : 4
Schlafli Type : {8,6,5}
Number of vertices, edges, etc : 8, 48, 30, 10
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,6,5,2} of size 1920
Vertex Figure Of :
{2,8,6,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,5}*480a
4-fold quotients : {2,6,5}*240a
Covers (Minimal Covers in Boldface) :
2-fold covers : {16,6,5}*1920a, {8,6,5}*1920a, {8,6,10}*1920c, {8,6,10}*1920d
Permutation Representation (GAP) :
```s0 := (1,2)(3,4)(5,8)(6,7);;
s1 := ( 2, 7)( 3, 5)( 6, 8)(12,13);;
s2 := ( 9,10)(11,12);;
s3 := (10,11)(12,13);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*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*s3*s2*s1*s3*s2*s3*s2*s1*s3*s2*s1*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope