# Polytope of Type {10,40}

Atlas Canonical Name : {10,40}*960a
if this polytope has a name.
Group : SmallGroup(960,5739)
Rank : 3
Schlafli Type : {10,40}
Number of vertices, edges, etc : 12, 240, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,40,2} of size 1920
Vertex Figure Of :
{2,10,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,20}*480a
4-fold quotients : {10,10}*240a
8-fold quotients : {5,10}*120b, {10,5}*120b
16-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,80}*1920a, {10,80}*1920b, {10,40}*1920a
Permutation Representation (GAP) :
```s0 := (10,11)(12,13);;
s1 := ( 2, 4)( 3, 6)( 5, 8)( 9,10)(11,12);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)(10,12)(11,13);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;

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

```
References : None.
to this polytope