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# Chiral Polytope of Type {6,45}

Regular Cover :{6,45}*1620a with group SmallGroup(1620,131) = C5 ⋊ ((C3 x C9) ⋊ D6)of order 1620
Rank : 3
Schlafli Type : {6,45}
Rotation Group : SmallGroup(270,15) = C45 ⋊ C6 of order 270
Number of vertices, edges, etc : 6, 135, 45
If Aut({6,45}*1620a)=<s0, s1, s2>, then this chiral polytope is ({6,45}*1620a)/N, where
N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 3
Facet : (Regular) 6-gon
Vertex Figure : (Regular) 45-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :
```F := FreeGroup("sig1","sig2");;
sig1 := F.1;;  sig2 := F.2;;
rels := [ sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1, sig1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1,
sig1*sig2^-1*sig1^-1*sig1^-1*sig2^-1*sig1*sig2^-1*sig1*sig1*sig2^-1, sig1^-1*sig1^-1*sig2*sig2*sig2*sig1^-1*sig2^-1*sig2^-1*sig1^-1*sig2*sig2*sig2*sig2*sig2*sig2*sig2*sig2*sig2*sig2 ];;
rotpoly := F / rels;;

```
Finitely Presented Group Representation of the Rotation Group (Magma) :

```rotpoly<sig1,sig2> := Group< sig1,sig2 | sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig2^-1*sig2^-1*sig1*sig2^-1*sig2^-1, sig1*sig2^-1*sig1^-1*sig1^-1*sig2^-1*sig1*sig2^-1*sig1*sig1*sig2^-1,
sig1^-1*sig1^-1*sig2*sig2*sig2*sig1^-1*sig2^-1*sig2^-1*sig1^-1*sig2*sig2*sig2*sig2*sig2*sig2*sig2*sig2*sig2*sig2 >;

```