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# Polytope of Type {10,6}

Atlas Canonical Name : {10,6}*720b
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 3
Schlafli Type : {10,6}
Number of vertices, edges, etc : 60, 180, 36
Order of s0s1s2 : 30
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,6,2} of size 1440
Vertex Figure Of :
{2,10,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,3}*360
3-fold quotients : {10,6}*240c
6-fold quotients : {5,6}*120c, {10,3}*120b
12-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,12}*1440e, {10,12}*1440f, {10,6}*1440f
Permutation Representation (GAP) :
```s0 := ( 7, 8)( 9,10);;
s1 := (4,5)(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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope