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# Polytope of Type {5,10}

Atlas Canonical Name : {5,10}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5843)
Rank : 3
Schlafli Type : {5,10}
Number of vertices, edges, etc : 72, 360, 144
Order of s0s1s2 : 10
Order of s0s1s2s1 : 8
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 : {5,10}*720
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 6)( 4, 9)( 5, 7)( 8,10);;
s1 := ( 1, 2)( 3, 4)( 5,10)( 6, 7)( 8, 9);;
s2 := ( 1, 5)( 2, 8)( 3, 7)( 6,10)(11,12);;
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,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope