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# Polytope of Type {6,80}

Atlas Canonical Name : {6,80}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240471)
Rank : 3
Schlafli Type : {6,80}
Number of vertices, edges, etc : 12, 480, 160
Order of s0s1s2 : 80
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {6,40}*960a
4-fold quotients : {6,20}*480a
8-fold quotients : {6,10}*240c
16-fold quotients : {3,10}*120b, {6,5}*120c
32-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1,16)( 2,15)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(18,21)(19,20);;
s1 := ( 1,12)( 2,10)( 3,14)( 4, 8)( 5,16)( 7,15)( 9,13)(17,18)(19,20);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(18,20)(19,21);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope