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# Polytope of Type {15,6}

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

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

```
References : None.
to this polytope