# Polytope of Type {6,15}

Atlas Canonical Name : {6,15}*720d
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 3
Schlafli Type : {6,15}
Number of vertices, edges, etc : 24, 180, 60
Order of s0s1s2 : 30
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,15,2} of size 1440
Vertex Figure Of :
{2,6,15} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,15}*360
3-fold quotients : {6,5}*240b
6-fold quotients : {3,5}*120, {6,5}*120b, {6,5}*120c
12-fold quotients : {3,5}*60
60-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,15}*1440b, {6,30}*1440f
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 7, 8)( 9,10);;
s1 := ( 4, 5)( 6, 7)( 9,10);;
s2 := ( 3, 4)( 7, 9)( 8,10);;
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,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope