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Polytope of Type {10,70}

Atlas Canonical Name : {10,70}*1680b
if this polytope has a name.
Group : SmallGroup(1680,931)
Rank : 3
Schlafli Type : {10,70}
Number of vertices, edges, etc : 12, 420, 84
Order of s0s1s2 : 21
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,35}*840
7-fold quotients : {10,10}*240d
14-fold quotients : {5,10}*120a, {10,5}*120b
28-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 9,10)(11,12)(13,14);;
s1 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 9,11)(10,12)(13,14);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(14)!( 9,10)(11,12)(13,14);
s1 := Sym(14)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(14)!( 1, 2)( 3, 4)( 5, 6)( 9,11)(10,12)(13,14);
poly := sub<Sym(14)|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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*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 >;

```
References : None.
to this polytope