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# Chiral Polytope of Type {6,3}

Regular Cover :{6,3}*1764 with group SmallGroup(1764,146) = (C3 x C72) ⋊ D6of order 1764
Rank : 3
Schlafli Type : {6,3}
Rotation Group : SmallGroup(126,9) = C7 ⋊ (S3 x C3) of order 126
Number of vertices, edges, etc : 42, 63, 21
If Aut({6,3}*1764)=<s0, s1, s2>, then this chiral polytope is ({6,3}*1764)/N, where
N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 7
Facet : (Regular) 6-gon
Vertex Figure : (Regular) 3-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :
```F := FreeGroup("sig1","sig2");;
sig1 := F.1;;  sig2 := F.2;;
rels := [ sig2*sig2*sig2, sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig1*sig1*sig2*sig1^-1*sig1^-1*sig2*sig1^-1*sig1^-1*sig2^-1*sig1*sig2^-1*sig1*sig1*sig2^-1 ];;
rotpoly := F / rels;;

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

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

```