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# Polytope of Type {3,15}

Atlas Canonical Name : {3,15}*360
if this polytope has a name.
Group : SmallGroup(360,121)
Rank : 3
Schlafli Type : {3,15}
Number of vertices, edges, etc : 12, 90, 60
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 :
{3,15,2} of size 720
Vertex Figure Of :
{2,3,15} of size 720
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,5}*120
6-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,30}*720, {6,15}*720c
4-fold covers : {3,60}*1440, {12,15}*1440a, {3,15}*1440, {6,30}*1440e
5-fold covers : {15,15}*1800a
Permutation Representation (GAP) :
```s0 := (2,3)(5,6)(7,8);;
s1 := (1,2)(4,5)(7,8);;
s2 := (2,3)(5,7)(6,8);;
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,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope