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# Polytope of Type {10,15}

Atlas Canonical Name : {10,15}*1200a
if this polytope has a name.
Group : SmallGroup(1200,944)
Rank : 3
Schlafli Type : {10,15}
Number of vertices, edges, etc : 40, 300, 60
Order of s0s1s2 : 10
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,15}*600
5-fold quotients : {10,3}*240
10-fold quotients : {5,3}*120, {10,3}*120a, {10,3}*120b
20-fold quotients : {5,3}*60
60-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 7, 8)( 9,10)(11,12);;
s1 := (2,4)(3,5)(6,7)(8,9);;
s2 := ( 1, 2)( 3, 4)( 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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope