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# Polytope of Type {15,3}

Atlas Canonical Name : {15,3}*360
if this polytope has a name.
Group : SmallGroup(360,121)
Rank : 3
Schlafli Type : {15,3}
Number of vertices, edges, etc : 60, 90, 12
Order of s0s1s2 : 10
Order of s0s1s2s1 : 15
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{15,3,2} of size 720
Vertex Figure Of :
{2,15,3} of size 720
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {5,3}*120
6-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {15,6}*720d, {30,3}*720
4-fold covers : {15,12}*1440a, {60,3}*1440, {15,3}*1440, {30,6}*1440f
5-fold covers : {15,15}*1800b
Permutation Representation (GAP) :
```s0 := (2,3)(5,6)(7,8);;
s1 := (1,2)(4,5)(6,7);;
s2 := (2,3)(5,8)(6,7);;
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, 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*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope